5xy(2x+3y)(2x-3y)=

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Solution for 5xy(2x+3y)(2x-3y)= equation: 


Simplifying
5xy(2x + 3y)(2x + -3y) = 0

Multiply (2x + 3y) * (2x + -3y)
5xy(2x * (2x + -3y) + 3y * (2x + -3y)) = 0
5xy((2x * 2x + -3y * 2x) + 3y * (2x + -3y)) = 0

Reorder the terms:
5xy((-6xy + 4x2) + 3y * (2x + -3y)) = 0
5xy((-6xy + 4x2) + 3y * (2x + -3y)) = 0
5xy(-6xy + 4x2 + (2x * 3y + -3y * 3y)) = 0
5xy(-6xy + 4x2 + (6xy + -9y2)) = 0

Reorder the terms:
5xy(-6xy + 6xy + 4x2 + -9y2) = 0

Combine like terms: -6xy + 6xy = 0
5xy(0 + 4x2 + -9y2) = 0
5xy(4x2 + -9y2) = 0
(4x2 * 5xy + -9y2 * 5xy) = 0

Reorder the terms:
(-45xy3 + 20x3y) = 0
(-45xy3 + 20x3y) = 0

Solving
-45xy3 + 20x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5xy'.
5xy(-9y2 + 4x2) = 0

Factor a difference between two squares.
5xy((3y + 2x)(-3y + 2x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve:

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 0

The solution to this equation could not be determined.

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

Subproblem 2
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

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 = {-1.5y, 1.5y}

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