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(2x-1)(x+5)+(2x-1)(x-2)=0

2 min read Jun 16, 2024
(2x-1)(x+5)+(2x-1)(x-2)=0

Solving the Equation (2x-1)(x+5) + (2x-1)(x-2) = 0

This equation involves factoring and simplification to find the solutions for x. Let's break down the steps:

1. Factoring out the common term

Notice that both terms on the left side of the equation share the common factor (2x-1). We can factor this out:

(2x-1)(x+5) + (2x-1)(x-2) = 0

(2x-1)[(x+5) + (x-2)] = 0

2. Simplifying the expression

Now we simplify the expression inside the square brackets:

(2x-1)[2x + 3] = 0

3. Applying the Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero. This means we have two possibilities:

  • 2x - 1 = 0
  • 2x + 3 = 0

4. Solving for x

Let's solve each equation separately:

  • 2x - 1 = 0

    • 2x = 1
    • x = 1/2

  • 2x + 3 = 0

    • 2x = -3
    • x = -3/2

Therefore, the solutions to the equation (2x-1)(x+5) + (2x-1)(x-2) = 0 are x = 1/2 and x = -3/2.

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