x(x+3)=2x(6-x)

Solution for x(x+3)=2x(6-x) equation:

Simplifying
x(x + 3) = 2x(6 + -1x)

Reorder the terms:
x(3 + x) = 2x(6 + -1x)
(3 * x + x * x) = 2x(6 + -1x)
(3x + x2) = 2x(6 + -1x)
3x + x2 = (6 * 2x + -1x * 2x)
3x + x2 = (12x + -2x2)

Solving
3x + x2 = 12x + -2x2

Solving for variable 'x'.

Reorder the terms:
3x + -12x + x2 + 2x2 = 12x + -2x2 + -12x + 2x2

Combine like terms: 3x + -12x = -9x
-9x + x2 + 2x2 = 12x + -2x2 + -12x + 2x2

Combine like terms: x2 + 2x2 = 3x2
-9x + 3x2 = 12x + -2x2 + -12x + 2x2

Reorder the terms:
-9x + 3x2 = 12x + -12x + -2x2 + 2x2

Combine like terms: 12x + -12x = 0
-9x + 3x2 = 0 + -2x2 + 2x2
-9x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-9x + 3x2 = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

Simplifying
x = 3
Solution
x = {0, 3}