4x^2+32x=-64

Solution for 4x^2+32x=-64 equation:

Simplifying
4x2 + 32x = -64

Reorder the terms:
32x + 4x2 = -64

Solving
32x + 4x2 = -64

Solving for variable 'x'.

Reorder the terms:
64 + 32x + 4x2 = -64 + 64

Combine like terms: -64 + 64 = 0
64 + 32x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + 8x + x2) = 0

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

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

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-4, -4}