-x^2+32x-220=0

Solution for -x^2+32x-220=0 equation:

Simplifying
-1x2 + 32x + -220 = 0

Reorder the terms:
-220 + 32x + -1x2 = 0

Solving
-220 + 32x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-22 + x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-22 + x)' equal to zero and attempt to solve:

Simplifying
-22 + x = 0

Solving
-22 + x = 0

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

Add '22' to each side of the equation.
-22 + 22 + x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + x = 0 + 22
x = 0 + 22

Combine like terms: 0 + 22 = 22
x = 22

Simplifying
x = 22
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {22, 10}