32=16x-2x^2

Solution for 32=16x-2x^2 equation:

Simplifying
32 = 16x + -2x2

Solving
32 = 16x + -2x2

Solving for variable 'x'.

Reorder the terms:
32 + -16x + 2x2 = 16x + -16x + -2x2 + 2x2

Combine like terms: 16x + -16x = 0
32 + -16x + 2x2 = 0 + -2x2 + 2x2
32 + -16x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
32 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -8x + x2) = 0

Factor a trinomial.
2((4 + -1x)(4 + -1x)) = 0

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {4, 4}