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Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     m^2-(q^2*r^2*b^2/v^2)=0 

Step  1  :

            b2
 Simplify   ——
            v2

Equation at the end of step  1  :

                    b2
  (m2)-(((q2)•(r2))•——)  = 0 
                    v2
 Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  v²  as the denominator :

           m2     m2 • v2
     m2 =  ——  =  ———————
           1        v2   

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 :

 2.2       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:

 m2 • v2 - (q2r2b2)      m2v2 - q2r2b2 
 ——————————————————  =  —————————————
         v2                  v2      

Trying to factor as a Difference of Squares :

 2.3      Factoring:  m²v² - q²r²b² 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  m²  is the square of  m¹ 

Check :  v²  is the square of  v¹ 

Check :  q²  is the square of  q¹ 

Check :  r²  is the square of  r¹ 

Check :  b²  is the square of  b¹ 

Factorization is :       (mv + qrb)  •  (mv - qrb) 

Equation at the end of step  2  :

  (mv + qrb) • (mv - qrb)
  ———————————————————————  = 0 
            v2           

Step  3  :

When a fraction equals zero :

 3.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  (mv+qrb)•(mv-qrb)
  ————————————————— • v2 = 0 • v2
         v2        

Now, on the left hand side, the  v²  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   (mv+qrb)  •  (mv-qrb)  = 0

Theory - Roots of a product :

 3.2    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 3.3     Solve   mv+qrb  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

Solving a Single Variable Equation :

 3.4     Solve   mv-qrb  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

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