(4x-6y)(2x+8y)=

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Solution for (4x-6y)(2x+8y)= equation: 


Simplifying
(4x + -6y)(2x + 8y) = 0

Multiply (4x + -6y) * (2x + 8y)
(4x * (2x + 8y) + -6y * (2x + 8y)) = 0
((2x * 4x + 8y * 4x) + -6y * (2x + 8y)) = 0

Reorder the terms:
((32xy + 8x2) + -6y * (2x + 8y)) = 0
((32xy + 8x2) + -6y * (2x + 8y)) = 0
(32xy + 8x2 + (2x * -6y + 8y * -6y)) = 0
(32xy + 8x2 + (-12xy + -48y2)) = 0

Reorder the terms:
(32xy + -12xy + 8x2 + -48y2) = 0

Combine like terms: 32xy + -12xy = 20xy
(20xy + 8x2 + -48y2) = 0

Solving
20xy + 8x2 + -48y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5xy + 2x2 + -12y2) = 0

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

Ignore the factor 4.

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 + 4y)' equal to zero and attempt to solve:

Simplifying
x + 4y = 0

Solving
x + 4y = 0

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

Add '-4y' to each side of the equation.
x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
x + 0 = 0 + -4y
x = 0 + -4y
Remove the zero:
x = -4y

Simplifying
x = -4y
Solution
x = {1.5y, -4y}

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