0=4x^2+24x+32

Solution for 0=4x^2+24x+32 equation:

Simplifying
0 = 4x2 + 24x + 32

Reorder the terms:
0 = 32 + 24x + 4x2

Solving
0 = 32 + 24x + 4x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-4'.
-4(8 + 6x + x2) = 0

Factor a trinomial.
-4((4 + x)(2 + 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 '(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 = {-4, -2}