12x^3-2x^2-24xy^2=

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Solution for 12x^3-2x^2-24xy^2= equation: 


Simplifying
12x3 + -2x2 + -24xy2 = 0

Reorder the terms:
-24xy2 + -2x2 + 12x3 = 0

Solving
-24xy2 + -2x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-12y2 + -1x + 6x2) = 0

Factor a trinomial.
2x((-4y + -3x)(3y + -2x)) = 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 '(-4y + -3x)' equal to zero and attempt to solve:

Simplifying
-4y + -3x = 0

Reorder the terms:
-3x + -4y = 0

Solving
-3x + -4y = 0

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

Add '4y' to each side of the equation.
-3x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
-3x + 0 = 0 + 4y
-3x = 0 + 4y
Remove the zero:
-3x = 4y

Divide each side by '-3'.
x = -1.333333333y

Simplifying
x = -1.333333333y

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

Simplifying
3y + -2x = 0

Reorder the terms:
-2x + 3y = 0

Solving
-2x + 3y = 0

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

Add '-3y' to each side of the equation.
-2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
-2x + 0 = 0 + -3y
-2x = 0 + -3y
Remove the zero:
-2x = -3y

Divide each side by '-2'.
x = 1.5y

Simplifying
x = 1.5y
Solution
x = {0, -1.333333333y, 1.5y}

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