(x-4)(x+2)-(x-5)(x+6)=-x

2 min read Jun 17, 2024
(x-4)(x+2)-(x-5)(x+6)=-x

Solving the Equation: (x-4)(x+2)-(x-5)(x+6)=-x

This article will guide you through solving the equation (x-4)(x+2)-(x-5)(x+6)=-x. We will use the distributive property and combine like terms to find the solution.

Expanding the Equation

First, we need to expand the equation by multiplying the terms in the parentheses:

  • (x-4)(x+2): x² + 2x - 4x - 8 = x² - 2x - 8
  • (x-5)(x+6): x² + 6x - 5x - 30 = x² + x - 30

Now, substitute the expanded terms back into the original equation:

(x² - 2x - 8) - (x² + x - 30) = -x

Simplifying the Equation

Next, simplify the equation by removing the parentheses and combining like terms:

x² - 2x - 8 - x² - x + 30 = -x

-3x + 22 = -x

Solving for x

Finally, solve for x by isolating the variable:

-3x + x = -22

-2x = -22

x = -22 / -2

x = 11

Conclusion

Therefore, the solution to the equation (x-4)(x+2)-(x-5)(x+6)=-x is x = 11. You can verify this solution by substituting it back into the original equation and confirming that both sides are equal.

Featured Posts