110=-2x^2+32x

Solution for 110=-2x^2+32x equation:

Simplifying
110 = -2x2 + 32x

Reorder the terms:
110 = 32x + -2x2

Solving
110 = 32x + -2x2

Solving for variable 'x'.

Reorder the terms:
110 + -32x + 2x2 = 32x + -32x + -2x2 + 2x2

Combine like terms: 32x + -32x = 0
110 + -32x + 2x2 = 0 + -2x2 + 2x2
110 + -32x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
110 + -32x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(55 + -16x + x2) = 0

Factor a trinomial.
2((5 + -1x)(11 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {5, 11}