0=-16x^2+96x-108

Solution for 0=-16x^2+96x-108 equation:

Simplifying
0 = -16x2 + 96x + -108

Reorder the terms:
0 = -108 + 96x + -16x2

Solving
0 = -108 + 96x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + 108 = 108
108 + -96x + 16x2 = -108 + 96x + -16x2 + 108 + -96x + 16x2

Reorder the terms:
108 + -96x + 16x2 = -108 + 108 + 96x + -96x + -16x2 + 16x2

Combine like terms: -108 + 108 = 0
108 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2
108 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2

Combine like terms: 96x + -96x = 0
108 + -96x + 16x2 = 0 + -16x2 + 16x2
108 + -96x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
108 + -96x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(27 + -24x + 4x2) = 0

Factor a trinomial.
4((3 + -2x)(9 + -2x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {1.5, 4.5}