Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.12" was replaced by "(12/100)". 2 more similar replacement(s)

Step  1  :

             3
 Simplify   ——
            25

Equation at the end of step  1  :

    49                    3
  ((—— • (t2)) -  4t) -  ——
    10                   25
 Step  2  :
            49
 Simplify   ——
            10

Equation at the end of step  2  :

    49                  3
  ((—— • t2) -  4t) -  ——
    10                 25

Step  3  :

Equation at the end of step  3  :

   49t2            3
  (———— -  4t) -  ——
    10            25

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  10  as the denominator :

          4t     4t • 10
    4t =  ——  =  ———————
          1        10   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 49t2 - (4t • 10)     49t2 - 40t
 ————————————————  =  ——————————
        10                10    

Equation at the end of step  4  :

  (49t2 - 40t)     3
  ———————————— -  ——
       10         25

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   49t² - 40t  =   t • (49t - 40) 

Calculating the Least Common Multiple :

 6.2    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       25 

      Least Common Multiple:
      50 

Calculating Multipliers :

 6.3    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 5

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 6.4      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      t • (49t-40) • 5
   ——————————————————  =   ————————————————
         L.C.M                    50       

   R. Mult. • R. Num.      3 • 2
   ——————————————————  =   —————
         L.C.M              50  

Adding fractions that have a common denominator :

 6.5       Adding up the two equivalent fractions

 t • (49t-40) • 5 - (3 • 2)     245t2 - 200t - 6
 ——————————————————————————  =  ————————————————
             50                        50       

Trying to factor by splitting the middle term

 6.6     Factoring  245t² - 200t - 6 

The first term is,  245t²  its coefficient is  245 .
The middle term is,  -200t  its coefficient is  -200 .
The last term, "the constant", is  -6 

Step-1 : Multiply the coefficient of the first term by the constant   245 • -6 = -1470 

Step-2 : Find two factors of  -1470  whose sum equals the coefficient of the middle term, which is   -200 .

For tidiness, printing of 18 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  245t2 - 200t - 6
  ————————————————
         50