(-10x-8y)(8x-10y)=0

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Solution for (-10x-8y)(8x-10y)=0 equation: 


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

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

Reorder the terms:
((100xy + -80x2) + -8y * (8x + -10y)) = 0
((100xy + -80x2) + -8y * (8x + -10y)) = 0
(100xy + -80x2 + (8x * -8y + -10y * -8y)) = 0
(100xy + -80x2 + (-64xy + 80y2)) = 0

Reorder the terms:
(100xy + -64xy + -80x2 + 80y2) = 0

Combine like terms: 100xy + -64xy = 36xy
(36xy + -80x2 + 80y2) = 0

Solving
36xy + -80x2 + 80y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(9xy + -20x2 + 20y2) = 0

Factor a trinomial.
4((-5x + -4y)(4x + -5y)) = 0

Ignore the factor 4.

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 '(4x + -5y)' equal to zero and attempt to solve:

Simplifying
4x + -5y = 0

Solving
4x + -5y = 0

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

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

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

Divide each side by '4'.
x = 1.25y

Simplifying
x = 1.25y
Solution
x = {-0.8y, 1.25y}

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