(x-8)(4x+3)-(x-8)(x-2)=0

2 min read Jun 17, 2024

Solving the Equation: (x-8)(4x+3)-(x-8)(x-2)=0

This equation presents a scenario where we need to solve for the value(s) of 'x' that make the equation true. Let's break down the steps to find the solution.

1. Factor out the common term

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

(x-8) [(4x+3) - (x-2)] = 0

2. Simplify the expression inside the brackets

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

(x-8) (4x + 3 - x + 2) = 0 (x-8) (3x + 5) = 0

3. Apply 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 have two possible scenarios:

Scenario 1: (x-8) = 0
Scenario 2: (3x + 5) = 0

4. Solve for x in each scenario

Scenario 1:
- x - 8 = 0
- x = 8
Scenario 2:
- 3x + 5 = 0
- 3x = -5
- x = -5/3

5. Solution

Therefore, the solutions to the equation (x-8)(4x+3)-(x-8)(x-2)=0 are:

x = 8
x = -5/3