(x+1)(x-4)=6

2 min read Jun 16, 2024

Solving the Equation (x+1)(x-4) = 6

This article will guide you through the steps of solving the equation (x+1)(x-4) = 6.

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

(x+1)(x-4) = x² - 4x + x - 4

This simplifies to:

x² - 3x - 4 = 6

Next, we need to move all the terms to one side of the equation to set it equal to zero:

x² - 3x - 4 - 6 = 0

This gives us:

x² - 3x - 10 = 0

Now we can factor the quadratic equation. We need to find two numbers that multiply to -10 and add up to -3. These numbers are -5 and 2:

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

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

x - 5 = 0 or x + 2 = 0

Solving for x in each case:

x = 5 or x = -2

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

For x = 5:

(5 + 1)(5 - 4) = 6(6)(1) = 6

For x = -2:

(-2 + 1)(-2 - 4) = (-1)(-6) = 6

Therefore, the solutions x = 5 and x = -2 are both valid solutions to the equation (x+1)(x-4) = 6.