Solution - Linear equations with one unknown

Rearrange:

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

                -4*k^2-8*k-3-(-3-5*k^2)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (((0-(4•(k2)))-8k)-3)-(-3-5k2)  = 0 
 Step  2  :

Equation at the end of step  2  :

  (((0 -  22k2) -  8k) -  3) -  (-5k2 - 3)  = 0 

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   k² - 8k  =   k • (k - 8) 

Equation at the end of step  4  :

  k • (k - 8)  = 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  :    k = 0 

  Solution is  k = 0

Solving a Single Variable Equation :

 5.3      Solve  :    k-8 = 0 

 Add  8  to both sides of the equation : 
                      k = 8

Two solutions were found :

1.  k = 8
2.  k = 0