575=120x-x^2

Solution for 575=120x-x^2 equation:

Simplifying
575 = 120x + -1x2

Solving
575 = 120x + -1x2

Solving for variable 'x'.

Reorder the terms:
575 + -120x + x2 = 120x + -120x + -1x2 + x2

Combine like terms: 120x + -120x = 0
575 + -120x + x2 = 0 + -1x2 + x2
575 + -120x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
575 + -120x + x2 = 0

Factor a trinomial.
(5 + -1x)(115 + -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 '(115 + -1x)' equal to zero and attempt to solve:

Simplifying
115 + -1x = 0

Solving
115 + -1x = 0

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

Add '-115' to each side of the equation.
115 + -115 + -1x = 0 + -115

Combine like terms: 115 + -115 = 0
0 + -1x = 0 + -115
-1x = 0 + -115

Combine like terms: 0 + -115 = -115
-1x = -115

Divide each side by '-1'.
x = 115

Simplifying
x = 115
Solution
x = {5, 115}