0=4x^2+32x+48

Solution for 0=4x^2+32x+48 equation:

Simplifying
0 = 4x2 + 32x + 48

Reorder the terms:
0 = 48 + 32x + 4x2

Solving
0 = 48 + 32x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -48 = -48
-48 + -32x + -4x2 = 48 + 32x + 4x2 + -48 + -32x + -4x2

Reorder the terms:
-48 + -32x + -4x2 = 48 + -48 + 32x + -32x + 4x2 + -4x2

Combine like terms: 48 + -48 = 0
-48 + -32x + -4x2 = 0 + 32x + -32x + 4x2 + -4x2
-48 + -32x + -4x2 = 32x + -32x + 4x2 + -4x2

Combine like terms: 32x + -32x = 0
-48 + -32x + -4x2 = 0 + 4x2 + -4x2
-48 + -32x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-48 + -32x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(12 + 8x + x2) = 0

Factor a trinomial.
-4((6 + x)(2 + x)) = 0

Ignore the factor -4.
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}