2(x^2)=-24-16x

Solution for 2(x^2)=-24-16x equation:

Simplifying
2(x2) = -24 + -16x

Solving
2x2 = -24 + -16x

Solving for variable 'x'.

Reorder the terms:
24 + 16x + 2x2 = -24 + -16x + 24 + 16x

Reorder the terms:
24 + 16x + 2x2 = -24 + 24 + -16x + 16x

Combine like terms: -24 + 24 = 0
24 + 16x + 2x2 = 0 + -16x + 16x
24 + 16x + 2x2 = -16x + 16x

Combine like terms: -16x + 16x = 0
24 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 8x + x2) = 0

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

Ignore the factor 2.
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}