(8x+3y)(6x-12y)=

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Solution for (8x+3y)(6x-12y)= equation: 


Simplifying
(8x + 3y)(6x + -12y) = 0

Multiply (8x + 3y) * (6x + -12y)
(8x * (6x + -12y) + 3y * (6x + -12y)) = 0
((6x * 8x + -12y * 8x) + 3y * (6x + -12y)) = 0

Reorder the terms:
((-96xy + 48x2) + 3y * (6x + -12y)) = 0
((-96xy + 48x2) + 3y * (6x + -12y)) = 0
(-96xy + 48x2 + (6x * 3y + -12y * 3y)) = 0
(-96xy + 48x2 + (18xy + -36y2)) = 0

Reorder the terms:
(-96xy + 18xy + 48x2 + -36y2) = 0

Combine like terms: -96xy + 18xy = -78xy
(-78xy + 48x2 + -36y2) = 0

Solving
-78xy + 48x2 + -36y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-13xy + 8x2 + -6y2) = 0

Factor a trinomial.
6((x + -2y)(8x + 3y)) = 0

Ignore the factor 6.

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 '(8x + 3y)' equal to zero and attempt to solve:

Simplifying
8x + 3y = 0

Solving
8x + 3y = 0

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

Add '-3y' to each side of the equation.
8x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
8x + 0 = 0 + -3y
8x = 0 + -3y
Remove the zero:
8x = -3y

Divide each side by '8'.
x = -0.375y

Simplifying
x = -0.375y
Solution
x = {2y, -0.375y}

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