(5x-3)(2x+1) (2x+1)(x-4)

Jasonbradley

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Jun 16, 2024

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Factoring and Solving the Equation (5x-3)(2x+1) = (2x+1)(x-4)

This problem involves factoring and solving an equation. Let's break it down step by step:

1. Factoring the Equation

We have:

(5x-3)(2x+1) = (2x+1)(x-4)

Notice that both sides of the equation share a common factor of (2x+1). We can simplify by dividing both sides by (2x+1), but we need to be careful about the case where (2x+1) = 0.

Important Note: Dividing by (2x+1) is valid only if (2x+1) ≠ 0.

2. Solving for x

Case 1: (2x+1) ≠ 0

Dividing both sides by (2x+1), we get:

5x - 3 = x - 4

Solving for x:

4x = -1

x = -1/4

Case 2: (2x+1) = 0

If (2x+1) = 0, then x = -1/2.

This value of x makes the original equation true, even though we divided by zero. It's a special case that needs to be considered.

3. Solutions

Therefore, the solutions to the equation (5x-3)(2x+1) = (2x+1)(x-4) are:

• x = -1/4
• x = -1/2

In conclusion, we found two solutions for the given equation by factoring and carefully considering the cases where the common factor might be zero.