(2x+3y)(4x-8y)=

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Solution for (2x+3y)(4x-8y)= equation: 


Simplifying
(2x + 3y)(4x + -8y) = 0

Multiply (2x + 3y) * (4x + -8y)
(2x * (4x + -8y) + 3y * (4x + -8y)) = 0
((4x * 2x + -8y * 2x) + 3y * (4x + -8y)) = 0

Reorder the terms:
((-16xy + 8x2) + 3y * (4x + -8y)) = 0
((-16xy + 8x2) + 3y * (4x + -8y)) = 0
(-16xy + 8x2 + (4x * 3y + -8y * 3y)) = 0
(-16xy + 8x2 + (12xy + -24y2)) = 0

Reorder the terms:
(-16xy + 12xy + 8x2 + -24y2) = 0

Combine like terms: -16xy + 12xy = -4xy
(-4xy + 8x2 + -24y2) = 0

Solving
-4xy + 8x2 + -24y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1xy + 2x2 + -6y2) = 0

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

Ignore the factor 4.

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 '(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 = {2y, -1.5y}

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