1100=120x-x^2

Solution for 1100=120x-x^2 equation:

Simplifying
1100 = 120x + -1x2

Solving
1100 = 120x + -1x2

Solving for variable 'x'.

Reorder the terms:
1100 + -120x + x2 = 120x + -120x + -1x2 + x2

Combine like terms: 120x + -120x = 0
1100 + -120x + x2 = 0 + -1x2 + x2
1100 + -120x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1100 + -120x + x2 = 0

Factor a trinomial.
(10 + -1x)(110 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(110 + -1x)' equal to zero and attempt to solve:

Simplifying
110 + -1x = 0

Solving
110 + -1x = 0

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

Add '-110' to each side of the equation.
110 + -110 + -1x = 0 + -110

Combine like terms: 110 + -110 = 0
0 + -1x = 0 + -110
-1x = 0 + -110

Combine like terms: 0 + -110 = -110
-1x = -110

Divide each side by '-1'.
x = 110

Simplifying
x = 110
Solution
x = {10, 110}