Chapter 4.8, Problem 3MRE

To determine

To find: the solution of the equation

Answer to Problem 3MRE

The solution of the equation is $\boxed{x=-42}$

Explanation of Solution

Given information: $\left(x-6\right)\left(x+9\right)=\left(x+6\right)\left(x-2\right)$

Concept Involved:

Solve the equation by getting the variable in one side of the equation and undoing whatever is done to it by performing reverse operation. The solution to the equation is the value of x that makes the equation TRUE.

Calculation:

Multiply first outer inner last terms in both sides of the equation

  $x^2+9x-6x-54=x^2-2x+6x-12$

Combine like terms on both sides of the equation

  $x^2+3x-54=x^2+4x-12$

In the process of getting x alone in one side of the equation we need to subtract $x^2\&4x$ on both sides of the equation

  $x^2+3x-54-x^2-4x=x^2+4x-12-x^2-4x$

Group and combine like terms on both sides of the equation

  $-x-54=-12$

Add 54 on both sides of the equation

  $-x-54+54=-12+54$

Combine like terms on both sides of the equation

  $-x=42$

Divide -1 on both sides of the equation

  $\frac{-x}{-1}=\frac{42}{-1}$

Simplify fraction on both sides of the equation

  $x=-42$

Conclusion:

The solution to the given equation $\left(x-6\right)\left(x+9\right)=\left(x+6\right)\left(x-2\right)$is $\boxed{x=-42}$