(x-3)*(x*3)=x(x-5)

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Solution for (x-3)*(x*3)=x(x-5) equation: 


Simplifying
(x + -3)(x * 3) = x(x + -5)

Reorder the terms:
(-3 + x)(x * 3) = x(x + -5)

Reorder the terms for easier multiplication:
(-3 + x)(3x) = x(x + -5)

Remove parenthesis around (3x)
(-3 + x) * 3x = x(x + -5)

Reorder the terms for easier multiplication:
3x(-3 + x) = x(x + -5)
(-3 * 3x + x * 3x) = x(x + -5)
(-9x + 3x2) = x(x + -5)

Reorder the terms:
-9x + 3x2 = x(-5 + x)
-9x + 3x2 = (-5 * x + x * x)
-9x + 3x2 = (-5x + x2)

Solving
-9x + 3x2 = -5x + x2

Solving for variable 'x'.

Reorder the terms:
-9x + 5x + 3x2 + -1x2 = -5x + x2 + 5x + -1x2

Combine like terms: -9x + 5x = -4x
-4x + 3x2 + -1x2 = -5x + x2 + 5x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-4x + 2x2 = -5x + x2 + 5x + -1x2

Reorder the terms:
-4x + 2x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
-4x + 2x2 = 0 + x2 + -1x2
-4x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4x + 2x2 = 0

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

Ignore the factor 2.

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

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

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

Simplifying
x = 2
Solution
x = {0, 2}

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