Answer: x = -6 and x = 9.
Explanation:
To solve the equation x² + x - 12 = x + 42 by factoring, follow these steps:
Start by moving all terms to one side of the equation to set it equal to zero:
x² + x - 12 - x - 42 = 0
Simplify the equation:
x² - 12 - 42 = 0
Combine like terms:
x² - 54 = 0
Factor the quadratic expression:
(x + 6)(x - 9) = 0
Set each factor equal to zero and solve for x:
x + 6 = 0
x - 9 = 0
Solve for x in each equation:
For x + 6 = 0:
x + 6 = 0
x = -6
For x - 9 = 0:
x - 9 = 0
x = 9
So, the solutions for the equation are x = -6 and x = 9.