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

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


Simplifying
(6x + -1y) * x(3x + -2y) = 0

Reorder the terms for easier multiplication:
x(6x + -1y)(3x + -2y) = 0

Multiply (6x + -1y) * (3x + -2y)
x(6x * (3x + -2y) + -1y * (3x + -2y)) = 0
x((3x * 6x + -2y * 6x) + -1y * (3x + -2y)) = 0

Reorder the terms:
x((-12xy + 18x2) + -1y * (3x + -2y)) = 0
x((-12xy + 18x2) + -1y * (3x + -2y)) = 0
x(-12xy + 18x2 + (3x * -1y + -2y * -1y)) = 0
x(-12xy + 18x2 + (-3xy + 2y2)) = 0

Reorder the terms:
x(-12xy + -3xy + 18x2 + 2y2) = 0

Combine like terms: -12xy + -3xy = -15xy
x(-15xy + 18x2 + 2y2) = 0
(-15xy * x + 18x2 * x + 2y2 * x) = 0

Reorder the terms:
(2xy2 + -15x2y + 18x3) = 0
(2xy2 + -15x2y + 18x3) = 0

Solving
2xy2 + -15x2y + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(2y2 + -15xy + 18x2) = 0

Factor a trinomial.
x((y + -6x)(2y + -3x)) = 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 '(y + -6x)' equal to zero and attempt to solve:

Simplifying
y + -6x = 0

Reorder the terms:
-6x + y = 0

Solving
-6x + y = 0

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

Add '-1y' to each side of the equation.
-6x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-6x + 0 = 0 + -1y
-6x = 0 + -1y
Remove the zero:
-6x = -1y

Divide each side by '-6'.
x = 0.1666666667y

Simplifying
x = 0.1666666667y

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

Simplifying
2y + -3x = 0

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

Solving
-3x + 2y = 0

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

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

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

Divide each side by '-3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y
Solution
x = {0, 0.1666666667y, 0.6666666667y}

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