Solve the equation by factoring. Show all of your work to receive full credit.
x^2+4x − 12=0
To solve the equation, we need to factor the quadratic expression.
x^2 + 4x - 12 = 0
To factor the quadratic expression, we need to find two numbers whose product is -12 and whose sum is 4. The numbers that satisfy these conditions are 6 and -2.
Therefore, we can rewrite the quadratic expression as:
(x + 6)(x - 2) = 0
Now, we can set each factor equal to 0 and solve for x:
x + 6 = 0
x = -6
x - 2 = 0
x = 2
Therefore, the equation is solved when x = -6 or x = 2.