3600=120x-x^2

Solution for 3600=120x-x^2 equation:

Simplifying
3600 = 120x + -1x2

Solving
3600 = 120x + -1x2

Solving for variable 'x'.

Reorder the terms:
3600 + -120x + x2 = 120x + -120x + -1x2 + x2

Combine like terms: 120x + -120x = 0
3600 + -120x + x2 = 0 + -1x2 + x2
3600 + -120x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
3600 + -120x + x2 = 0

Factor a trinomial.
(60 + -1x)(60 + -1x) = 0

Subproblem 1
Set the factor '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve:

Simplifying
60 + -1x = 0

Solving
60 + -1x = 0

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

Add '-60' to each side of the equation.
60 + -60 + -1x = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -1x = 0 + -60
-1x = 0 + -60

Combine like terms: 0 + -60 = -60
-1x = -60

Divide each side by '-1'.
x = 60

Simplifying
x = 60
Solution
x = {60, 60}