4x^2+24x+4=-32

Solution for 4x^2+24x+4=-32 equation:

Simplifying
4x2 + 24x + 4 = -32

Reorder the terms:
4 + 24x + 4x2 = -32

Solving
4 + 24x + 4x2 = -32

Solving for variable 'x'.

Reorder the terms:
4 + 32 + 24x + 4x2 = -32 + 32

Combine like terms: 4 + 32 = 36
36 + 24x + 4x2 = -32 + 32

Combine like terms: -32 + 32 = 0
36 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + 6x + x2) = 0

Factor a trinomial.
4((3 + x)(3 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-3, -3}