(12y+8x)(8y+10x)=

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Solution for (12y+8x)(8y+10x)= equation: 


Simplifying
(12y + 8x)(8y + 10x) = 0

Reorder the terms:
(8x + 12y)(8y + 10x) = 0

Reorder the terms:
(8x + 12y)(10x + 8y) = 0

Multiply (8x + 12y) * (10x + 8y)
(8x * (10x + 8y) + 12y * (10x + 8y)) = 0
((10x * 8x + 8y * 8x) + 12y * (10x + 8y)) = 0

Reorder the terms:
((64xy + 80x2) + 12y * (10x + 8y)) = 0
((64xy + 80x2) + 12y * (10x + 8y)) = 0
(64xy + 80x2 + (10x * 12y + 8y * 12y)) = 0
(64xy + 80x2 + (120xy + 96y2)) = 0

Reorder the terms:
(64xy + 120xy + 80x2 + 96y2) = 0

Combine like terms: 64xy + 120xy = 184xy
(184xy + 80x2 + 96y2) = 0

Solving
184xy + 80x2 + 96y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(23xy + 10x2 + 12y2) = 0

Factor a trinomial.
8((5x + 4y)(2x + 3y)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(5x + 4y)' equal to zero and attempt to solve:

Simplifying
5x + 4y = 0

Solving
5x + 4y = 0

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

Add '-4y' to each side of the equation.
5x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
5x + 0 = 0 + -4y
5x = 0 + -4y
Remove the zero:
5x = -4y

Divide each side by '5'.
x = -0.8y

Simplifying
x = -0.8y

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 = {-0.8y, -1.5y}

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