(6x^2+5xy^2)=(4xy-9x)(4xy)

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Solution for (6x^2+5xy^2)=(4xy-9x)(4xy) equation: 


Simplifying
(6x2 + 5xy2) = (4xy + -9x)(4xy)

Reorder the terms:
(5xy2 + 6x2) = (4xy + -9x)(4xy)

Remove parenthesis around (5xy2 + 6x2)
5xy2 + 6x2 = (4xy + -9x)(4xy)

Reorder the terms:
5xy2 + 6x2 = (-9x + 4xy)(4xy)

Remove parenthesis around (4xy)
5xy2 + 6x2 = (-9x + 4xy) * 4xy

Reorder the terms for easier multiplication:
5xy2 + 6x2 = 4xy(-9x + 4xy)
5xy2 + 6x2 = (-9x * 4xy + 4xy * 4xy)
5xy2 + 6x2 = (-36x2y + 16x2y2)

Solving
5xy2 + 6x2 = -36x2y + 16x2y2

Solving for variable 'x'.

Reorder the terms:
5xy2 + 6x2 + 36x2y + -16x2y2 = -36x2y + 36x2y + 16x2y2 + -16x2y2

Combine like terms: -36x2y + 36x2y = 0
5xy2 + 6x2 + 36x2y + -16x2y2 = 0 + 16x2y2 + -16x2y2
5xy2 + 6x2 + 36x2y + -16x2y2 = 16x2y2 + -16x2y2

Combine like terms: 16x2y2 + -16x2y2 = 0
5xy2 + 6x2 + 36x2y + -16x2y2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5y2 + 6x + 36xy + -16xy2) = 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 '(5y2 + 6x + 36xy + -16xy2)' equal to zero and attempt to solve:

Simplifying
5y2 + 6x + 36xy + -16xy2 = 0

Reorder the terms:
6x + 36xy + -16xy2 + 5y2 = 0

Solving
6x + 36xy + -16xy2 + 5y2 = 0

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

Add '-5y2' to each side of the equation.
6x + 36xy + -16xy2 + 5y2 + -5y2 = 0 + -5y2

Combine like terms: 5y2 + -5y2 = 0
6x + 36xy + -16xy2 + 0 = 0 + -5y2
6x + 36xy + -16xy2 = 0 + -5y2
Remove the zero:
6x + 36xy + -16xy2 = -5y2

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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