(9x-2y)(2x+3y)=

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


Simplifying
(9x + -2y)(2x + 3y) = 0

Multiply (9x + -2y) * (2x + 3y)
(9x * (2x + 3y) + -2y * (2x + 3y)) = 0
((2x * 9x + 3y * 9x) + -2y * (2x + 3y)) = 0

Reorder the terms:
((27xy + 18x2) + -2y * (2x + 3y)) = 0
((27xy + 18x2) + -2y * (2x + 3y)) = 0
(27xy + 18x2 + (2x * -2y + 3y * -2y)) = 0
(27xy + 18x2 + (-4xy + -6y2)) = 0

Reorder the terms:
(27xy + -4xy + 18x2 + -6y2) = 0

Combine like terms: 27xy + -4xy = 23xy
(23xy + 18x2 + -6y2) = 0

Solving
23xy + 18x2 + -6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(9x + -2y)(2x + 3y) = 0


Subproblem 1
Set the factor '(9x + -2y)' equal to zero and attempt to solve:

Simplifying
9x + -2y = 0

Solving
9x + -2y = 0

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

Add '2y' to each side of the equation.
9x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
9x + 0 = 0 + 2y
9x = 0 + 2y
Remove the zero:
9x = 2y

Divide each side by '9'.
x = 0.2222222222y

Simplifying
x = 0.2222222222y

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

Simplifying
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 = {0.2222222222y, -1.5y}

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