Solve the equation by factoring. Show all of your work to receive full credit.
x2+4x − 12=0
To solve the equation x^2 + 4x - 12 = 0 by factoring, we need to find two numbers that multiply to give -12 and add up to 4.
The factors of -12 are (-1, 12), (1, -12), (-2, 6), (2, -6), (-3, 4), and (3, -4).
Out of these pairs, the pair that adds up to 4 is (-2, 6).
Thus, we can rewrite the equation as (x - 2)(x + 6) = 0.
Setting each factor equal to zero, we have:
x - 2 = 0 or x + 6 = 0
Solving for x in each equation:
x = 2 or x = -6
Therefore, the solution to the equation x^2 + 4x - 12 = 0 is x = 2 or x = -6.