0=(120+x^2)-(200+11x)

Solution for 0=(120+x^2)-(200+11x) equation:

Simplifying
0 = (120 + x2) + -1(200 + 11x)

Remove parenthesis around (120 + x2)
0 = 120 + x2 + -1(200 + 11x)
0 = 120 + x2 + (200 * -1 + 11x * -1)
0 = 120 + x2 + (-200 + -11x)

Reorder the terms:
0 = 120 + -200 + -11x + x2

Combine like terms: 120 + -200 = -80
0 = -80 + -11x + x2

Solving
0 = -80 + -11x + x2

Solving for variable 'x'.

Combine like terms: 0 + 80 = 80
80 + 11x + -1x2 = -80 + -11x + x2 + 80 + 11x + -1x2

Reorder the terms:
80 + 11x + -1x2 = -80 + 80 + -11x + 11x + x2 + -1x2

Combine like terms: -80 + 80 = 0
80 + 11x + -1x2 = 0 + -11x + 11x + x2 + -1x2
80 + 11x + -1x2 = -11x + 11x + x2 + -1x2

Combine like terms: -11x + 11x = 0
80 + 11x + -1x2 = 0 + x2 + -1x2
80 + 11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
80 + 11x + -1x2 = 0

Factor a trinomial.
(16 + -1x)(5 + x) = 0

Subproblem 1
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {16, -5}