4x^2+16x+192=180

Solution for 4x^2+16x+192=180 equation:

Simplifying
4x2 + 16x + 192 = 180

Reorder the terms:
192 + 16x + 4x2 = 180

Solving
192 + 16x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
192 + -180 + 16x + 4x2 = 180 + -180

Combine like terms: 192 + -180 = 12
12 + 16x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
12 + 16x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 4x + x2) = 0

Factor a trinomial.
4((3 + x)(1 + 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-3, -1}