(2x-3y)(3x+6y)=0

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Solution for (2x-3y)(3x+6y)=0 equation: 


Simplifying
(2x + -3y)(3x + 6y) = 0

Multiply (2x + -3y) * (3x + 6y)
(2x * (3x + 6y) + -3y * (3x + 6y)) = 0
((3x * 2x + 6y * 2x) + -3y * (3x + 6y)) = 0

Reorder the terms:
((12xy + 6x2) + -3y * (3x + 6y)) = 0
((12xy + 6x2) + -3y * (3x + 6y)) = 0
(12xy + 6x2 + (3x * -3y + 6y * -3y)) = 0
(12xy + 6x2 + (-9xy + -18y2)) = 0

Reorder the terms:
(12xy + -9xy + 6x2 + -18y2) = 0

Combine like terms: 12xy + -9xy = 3xy
(3xy + 6x2 + -18y2) = 0

Solving
3xy + 6x2 + -18y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(xy + 2x2 + -6y2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

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

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

Simplifying
x = -2y
Solution
x = {1.5y, -2y}

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