(2x-1)(x+3)+(x+5)(2x-1)=0

Jasonbradley

2 min read

·

Jun 16, 2024

25

Share

Solving the Equation (2x-1)(x+3)+(x+5)(2x-1)=0

This article will guide you through the steps to solve the equation (2x-1)(x+3)+(x+5)(2x-1)=0.

1. Identifying Common Factors

First, notice that the expression (2x-1) appears in both terms of the equation. This is a common factor that can be factored out.

2. Factoring the Expression

We can rewrite the equation as:

(2x-1)(x+3) + (2x-1)(x+5) = 0

Now, factor out the common factor (2x-1):

(2x-1) [(x+3) + (x+5)] = 0

3. Simplifying the Expression

Simplify the expression inside the brackets:

(2x-1)(2x+8) = 0

4. Setting Factors to Zero

To find the solutions for x, we need to set each factor to zero:

(2x-1) = 0 or (2x+8) = 0

5. Solving for x

Solve each equation for x:

• 2x-1 = 0

  • 2x = 1
  • x = 1/2

• 2x+8 = 0

  • 2x = -8
  • x = -4

6. Conclusion

Therefore, the solutions to the equation (2x-1)(x+3)+(x+5)(2x-1)=0 are x = 1/2 and x = -4.