3(8x-7y)(3y-2x)=

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Solution for 3(8x-7y)(3y-2x)= equation: 


Simplifying
3(8x + -7y)(3y + -2x) = 0

Reorder the terms:
3(8x + -7y)(-2x + 3y) = 0

Multiply (8x + -7y) * (-2x + 3y)
3(8x * (-2x + 3y) + -7y * (-2x + 3y)) = 0
3((-2x * 8x + 3y * 8x) + -7y * (-2x + 3y)) = 0

Reorder the terms:
3((24xy + -16x2) + -7y * (-2x + 3y)) = 0
3((24xy + -16x2) + -7y * (-2x + 3y)) = 0
3(24xy + -16x2 + (-2x * -7y + 3y * -7y)) = 0
3(24xy + -16x2 + (14xy + -21y2)) = 0

Reorder the terms:
3(24xy + 14xy + -16x2 + -21y2) = 0

Combine like terms: 24xy + 14xy = 38xy
3(38xy + -16x2 + -21y2) = 0
(38xy * 3 + -16x2 * 3 + -21y2 * 3) = 0
(114xy + -48x2 + -63y2) = 0

Solving
114xy + -48x2 + -63y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(38xy + -16x2 + -21y2) = 0

Factor a trinomial.
3((-8x + 7y)(2x + -3y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8x + 7y)' equal to zero and attempt to solve:

Simplifying
-8x + 7y = 0

Solving
-8x + 7y = 0

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

Add '-7y' to each side of the equation.
-8x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
-8x + 0 = 0 + -7y
-8x = 0 + -7y
Remove the zero:
-8x = -7y

Divide each side by '-8'.
x = 0.875y

Simplifying
x = 0.875y

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 = {0.875y, 1.5y}

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