x^2=-4(2x+3)

Solution for x^2=-4(2x+3) equation:

Simplifying
x2 = -4(2x + 3)

Reorder the terms:
x2 = -4(3 + 2x)
x2 = (3 * -4 + 2x * -4)
x2 = (-12 + -8x)

Solving
x2 = -12 + -8x

Solving for variable 'x'.

Reorder the terms:
12 + 8x + x2 = -12 + -8x + 12 + 8x

Reorder the terms:
12 + 8x + x2 = -12 + 12 + -8x + 8x

Combine like terms: -12 + 12 = 0
12 + 8x + x2 = 0 + -8x + 8x
12 + 8x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
12 + 8x + x2 = 0

Factor a trinomial.
(6 + x)(2 + x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-6, -2}