x(240-3x)=3600

Solution for x(240-3x)=3600 equation:

Simplifying
x(240 + -3x) = 3600
(240 * x + -3x * x) = 3600
(240x + -3x2) = 3600

Solving
240x + -3x2 = 3600

Solving for variable 'x'.

Reorder the terms:
-3600 + 240x + -3x2 = 3600 + -3600

Combine like terms: 3600 + -3600 = 0
-3600 + 240x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1200 + 80x + -1x2) = 0

Factor a trinomial.
3((-60 + x)(20 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-60 + x)' equal to zero and attempt to solve:

Simplifying
-60 + x = 0

Solving
-60 + x = 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 + x = 0 + 60

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

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

Simplifying
x = 60
Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {60, 20}