2x+120+x^2-6x=180

Solution for 2x+120+x^2-6x=180 equation:

Simplifying
2x + 120 + x2 + -6x = 180

Reorder the terms:
120 + 2x + -6x + x2 = 180

Combine like terms: 2x + -6x = -4x
120 + -4x + x2 = 180

Solving
120 + -4x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
120 + -180 + -4x + x2 = 180 + -180

Combine like terms: 120 + -180 = -60
-60 + -4x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-60 + -4x + x2 = 0

Factor a trinomial.
(-6 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 10}