3600=3000+350x-50x^2

Solution for 3600=3000+350x-50x^2 equation:

Simplifying
3600 = 3000 + 350x + -50x2

Solving
3600 = 3000 + 350x + -50x2

Solving for variable 'x'.

Combine like terms: 3600 + -3000 = 600
600 + -350x + 50x2 = 3000 + 350x + -50x2 + -3000 + -350x + 50x2

Reorder the terms:
600 + -350x + 50x2 = 3000 + -3000 + 350x + -350x + -50x2 + 50x2

Combine like terms: 3000 + -3000 = 0
600 + -350x + 50x2 = 0 + 350x + -350x + -50x2 + 50x2
600 + -350x + 50x2 = 350x + -350x + -50x2 + 50x2

Combine like terms: 350x + -350x = 0
600 + -350x + 50x2 = 0 + -50x2 + 50x2
600 + -350x + 50x2 = -50x2 + 50x2

Combine like terms: -50x2 + 50x2 = 0
600 + -350x + 50x2 = 0

Factor out the Greatest Common Factor (GCF), '50'.
50(12 + -7x + x2) = 0

Factor a trinomial.
50((3 + -1x)(4 + -1x)) = 0

Ignore the factor 50.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {3, 4}