6xy^2-5xy-6x=0

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Solution for 6xy^2-5xy-6x=0 equation: 


Simplifying
6xy2 + -5xy + -6x = 0

Reorder the terms:
-6x + -5xy + 6xy2 = 0

Solving
-6x + -5xy + 6xy2 = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + -5y + 6y2) = 0

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

Simplifying
-2 + -3y = 0

Solving
-2 + -3y = 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 + -3y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3y = 0 + 2
-3y = 0 + 2

Combine like terms: 0 + 2 = 2
-3y = 2

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

Combine like terms: -3y + 3y = 0
0 = 2 + 3y

Simplifying
0 = 2 + 3y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

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

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

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

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

Combine like terms: -2y + 2y = 0
0 = -3 + 2y

Simplifying
0 = -3 + 2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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