(x-8)(5x+4)-(x-8)(2x+6)=0

Jasonbradley

2 min read Jun 17, 2024

Solving the Equation: (x-8)(5x+4)-(x-8)(2x+6)=0

This equation is a quadratic equation in disguise! Let's break it down step-by-step to find the solutions for x.

1. Factoring out the Common Factor

Notice that both terms on the left side of the equation have a common factor of (x-8). We can factor this out:

(x-8)(5x+4) - (x-8)(2x+6) = 0

(x-8)[(5x+4) - (2x+6)] = 0

2. Simplifying the Expression

Now, let's simplify the expression inside the brackets:

(x-8)(3x - 2) = 0

3. Applying the Zero Product Property

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for x:

x - 8 = 0
- Adding 8 to both sides, we get x = 8
3x - 2 = 0
- Adding 2 to both sides, we get 3x = 2
- Dividing both sides by 3, we get x = 2/3

4. Solutions

Therefore, the solutions to the equation (x-8)(5x+4)-(x-8)(2x+6)=0 are:

x = 8
x = 2/3