3x(6-x)=24

Solution for 3x(6-x)=24 equation:

Simplifying
3x(6 + -1x) = 24
(6 * 3x + -1x * 3x) = 24
(18x + -3x2) = 24

Solving
18x + -3x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 18x + -3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 6x + -1x2) = 0

Factor a trinomial.
3((-4 + x)(2 + -1x)) = 0

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

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {4, 2}