0=-3600+150x-x^2

Solution for 0=-3600+150x-x^2 equation:

Simplifying
0 = -3600 + 150x + -1x2

Solving
0 = -3600 + 150x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 3600 = 3600
3600 + -150x + x2 = -3600 + 150x + -1x2 + 3600 + -150x + x2

Reorder the terms:
3600 + -150x + x2 = -3600 + 3600 + 150x + -150x + -1x2 + x2

Combine like terms: -3600 + 3600 = 0
3600 + -150x + x2 = 0 + 150x + -150x + -1x2 + x2
3600 + -150x + x2 = 150x + -150x + -1x2 + x2

Combine like terms: 150x + -150x = 0
3600 + -150x + x2 = 0 + -1x2 + x2
3600 + -150x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
3600 + -150x + x2 = 0

Factor a trinomial.
(30 + -1x)(120 + -1x) = 0

Subproblem 1
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Subproblem 2
Set the factor '(120 + -1x)' equal to zero and attempt to solve:

Simplifying
120 + -1x = 0

Solving
120 + -1x = 0

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

Add '-120' to each side of the equation.
120 + -120 + -1x = 0 + -120

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

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

Divide each side by '-1'.
x = 120

Simplifying
x = 120
Solution
x = {30, 120}