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

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


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

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

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

Solving
6x + x2 = -3x + 3x2

Solving for variable 'x'.

Reorder the terms:
6x + 3x + x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: 6x + 3x = 9x
9x + x2 + -3x2 = -3x + 3x2 + 3x + -3x2

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + -2x) = 0


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 '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

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

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

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {0, 4.5}

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