Let's simplify the given equation step by step:

Let y = (x² + 2x)

Now, the equation becomes:
y² + 13y + 12 = 0

Now, we can factor this quadratic equation:
(y + 12)(y + 1) = 0

Now, we substitute back y = (x² + 2x):
(x² + 2x + 12)(x² + 2x + 1) = 0

Now, you can solve for x by setting each factor equal to zero:
x² + 2x + 12 = 0
x² + 2x + 1 = 0

Now solve each quadratic equation to find the values of x.