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

Jasonbradley

3 min read Jun 16, 2024

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

This article will guide you through the steps of solving the equation (2x-1)(x+3) = 4.

1. Expand the Equation

First, we need to expand the left side of the equation by multiplying the two binomials:

(2x-1)(x+3) = 2x² + 6x - x - 3

Simplifying, we get:

2x² + 5x - 3 = 4

2. Move all terms to one side

To solve this quadratic equation, we need to set it equal to zero. This is done by subtracting 4 from both sides:

2x² + 5x - 7 = 0

3. Factor the Quadratic Equation

Now we need to factor the quadratic expression on the left side. This can be done by finding two numbers that add up to 5 (the coefficient of the x term) and multiply to -14 (the product of the coefficient of the x² term and the constant term).

The numbers 7 and -2 satisfy these conditions:

7 + (-2) = 5 7 * (-2) = -14

Therefore, we can rewrite the equation as:

(2x - 2)(x + 7) = 0

4. Solve for x

For the product of two terms to be zero, at least one of the terms must be zero. So we have two possible solutions:

2x - 2 = 0 Solving for x, we get: x = 1
x + 7 = 0 Solving for x, we get: x = -7

5. Verification

To verify our solutions, we can substitute them back into the original equation:

For x = 1: (2(1) - 1)(1 + 3) = (1)(4) = 4 This solution is correct.
For x = -7: (2(-7) - 1)(-7 + 3) = (-15)(-4) = 60 ≠ 4 This solution is incorrect.

Conclusion

Therefore, the only valid solution to the equation (2x-1)(x+3) = 4 is x = 1.