(2xy-3x)(6xy+9x)=

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Solution for (2xy-3x)(6xy+9x)= equation: 


Simplifying
(2xy + -3x)(6xy + 9x) = 0

Reorder the terms:
(-3x + 2xy)(6xy + 9x) = 0

Reorder the terms:
(-3x + 2xy)(9x + 6xy) = 0

Multiply (-3x + 2xy) * (9x + 6xy)
(-3x * (9x + 6xy) + 2xy * (9x + 6xy)) = 0
((9x * -3x + 6xy * -3x) + 2xy * (9x + 6xy)) = 0
((-27x2 + -18x2y) + 2xy * (9x + 6xy)) = 0
(-27x2 + -18x2y + (9x * 2xy + 6xy * 2xy)) = 0
(-27x2 + -18x2y + (18x2y + 12x2y2)) = 0

Combine like terms: -18x2y + 18x2y = 0
(-27x2 + 0 + 12x2y2) = 0
(-27x2 + 12x2y2) = 0

Solving
-27x2 + 12x2y2 = 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), '3x2'.
3x2(-9 + 4y2) = 0

Factor a difference between two squares.
3x2((3 + 2y)(-3 + 2y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
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.

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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