120+x^2=200+11x

Solution for 120+x^2=200+11x equation:

Simplifying
120 + x2 = 200 + 11x

Solving
120 + x2 = 200 + 11x

Solving for variable 'x'.

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

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

Reorder the terms:
-80 + -11x + x2 = 200 + -200 + 11x + -11x

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

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

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

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 '(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
Solution
x = {-5, 16}