(x-4y)(8x-12y)=

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Solution for (x-4y)(8x-12y)= equation: 


Simplifying
(x + -4y)(8x + -12y) = 0

Multiply (x + -4y) * (8x + -12y)
(x(8x + -12y) + -4y * (8x + -12y)) = 0
((8x * x + -12y * x) + -4y * (8x + -12y)) = 0

Reorder the terms:
((-12xy + 8x2) + -4y * (8x + -12y)) = 0
((-12xy + 8x2) + -4y * (8x + -12y)) = 0
(-12xy + 8x2 + (8x * -4y + -12y * -4y)) = 0
(-12xy + 8x2 + (-32xy + 48y2)) = 0

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

Combine like terms: -12xy + -32xy = -44xy
(-44xy + 8x2 + 48y2) = 0

Solving
-44xy + 8x2 + 48y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-11xy + 2x2 + 12y2) = 0

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

Ignore the factor 4.

Subproblem 1
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

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 = {4y, 1.5y}

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