X2+5x=-2x-12 solve for x

X² + 5x = -2x -12
Add 2x to each side.
x² + 7x = -12
Add 12 to each side.
x² + 7x + 12 = 0
Let's solve this quadratic by factoring.
We want two numbers that add to get 7 and multiply to make 12. These are 3 and 4.
Split the middle of the quadratic.
x² + 3x + 4x + 12 = 0
Factor the first two and last two terms.
(You should get the same thing inside the parentheses.)
x(x+3) + 4(x+3) = 0
(x+4)(x+3) = 0
Any value of x which causes either factor to equal 0 is a solution.
We can derive the following equations and solutions:
x+4 = 0 ⇒ x = -4
x+3 = 0 ⇒ x = -3