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

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


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

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

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

Reorder the terms:
((4xy + -6x2) + 9y * (-3x + 2y)) = 0
((4xy + -6x2) + 9y * (-3x + 2y)) = 0
(4xy + -6x2 + (-3x * 9y + 2y * 9y)) = 0
(4xy + -6x2 + (-27xy + 18y2)) = 0

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

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

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

Solving for variable 'x'.

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


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

Simplifying
-2x + -9y = 0

Solving
-2x + -9y = 0

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

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

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

Divide each side by '-2'.
x = -4.5y

Simplifying
x = -4.5y

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

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

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

Combine like terms: -2y + 2y = 0
3x + 0 = 0 + 2y
3x = 0 + 2y
Remove the zero:
3x = 2y

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y
Solution
x = {-4.5y, 0.6666666667y}

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