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

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


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

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

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

Reorder the terms:
(6xy + -4xy + 2x2 + -12y2) = 0

Combine like terms: 6xy + -4xy = 2xy
(2xy + 2x2 + -12y2) = 0

Solving
2xy + 2x2 + -12y2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
2((x + -2y)(x + 3y)) = 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 '(x + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

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

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

Simplifying
x = -3y
Solution
x = {2y, -3y}

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