12x^3-12x^2y+3xy^2=

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Solution for 12x^3-12x^2y+3xy^2= equation:


Simplifying
12x3 + -12x2y + 3xy2 = 0

Reorder the terms:
3xy2 + -12x2y + 12x3 = 0

Solving
3xy2 + -12x2y + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(y2 + -4xy + 4x2) = 0

Factor a trinomial.
3x((y + -2x)(y + -2x)) = 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 '(y + -2x)' equal to zero and attempt to solve: Simplifying y + -2x = 0 Reorder the terms: -2x + y = 0 Solving -2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. -2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 -2x + 0 = 0 + -1y -2x = 0 + -1y Remove the zero: -2x = -1y Divide each side by '-2'. x = 0.5y Simplifying x = 0.5y

Subproblem 3

Set the factor '(y + -2x)' equal to zero and attempt to solve: Simplifying y + -2x = 0 Reorder the terms: -2x + y = 0 Solving -2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. -2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 -2x + 0 = 0 + -1y -2x = 0 + -1y Remove the zero: -2x = -1y Divide each side by '-2'. x = 0.5y Simplifying x = 0.5y

Solution

x = {0, 0.5y, 0.5y}

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