(2x-4y)(3x+2y)=

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Solution for (2x-4y)(3x+2y)= equation: 


Simplifying
(2x + -4y)(3x + 2y) = 0

Multiply (2x + -4y) * (3x + 2y)
(2x * (3x + 2y) + -4y * (3x + 2y)) = 0
((3x * 2x + 2y * 2x) + -4y * (3x + 2y)) = 0

Reorder the terms:
((4xy + 6x2) + -4y * (3x + 2y)) = 0
((4xy + 6x2) + -4y * (3x + 2y)) = 0
(4xy + 6x2 + (3x * -4y + 2y * -4y)) = 0
(4xy + 6x2 + (-12xy + -8y2)) = 0

Reorder the terms:
(4xy + -12xy + 6x2 + -8y2) = 0

Combine like terms: 4xy + -12xy = -8xy
(-8xy + 6x2 + -8y2) = 0

Solving
-8xy + 6x2 + -8y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4xy + 3x2 + -4y2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {2y, -0.6666666667y}

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