Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "p3"   was replaced by   "p^3". 

Rearrange:

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

                     5*p^2-7*p^3-(p^2)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  ((5 • (p2)) -  7p3) -  p2  = 0 
 Step  2  :

Equation at the end of step  2  :

  (5p2 -  7p3) -  p2  = 0 

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   4p² - 7p³  =   -p² • (7p - 4) 

Equation at the end of step  4  :

  -p2 • (7p - 4)  = 0 

Step  5  :

Theory - Roots of a product :

 5.1    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 :

 5.2      Solve  :    -p² = 0 

 Multiply both sides of the equation by (-1) :  p² = 0


 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      p  =  ± √ 0  

 Any root of zero is zero. This equation has one solution which is  p = 0

Solving a Single Variable Equation :

 5.3      Solve  :    7p-4 = 0 

 Add  4  to both sides of the equation : 
                      7p = 4
Divide both sides of the equation by 7:
                     p = 4/7 = 0.571

Two solutions were found :

1.  p = 4/7 = 0.571
   
2.  p = 0