(-3x-8y)(-5x-4y)=0

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Solution for (-3x-8y)(-5x-4y)=0 equation: 


Simplifying
(-3x + -8y)(-5x + -4y) = 0

Multiply (-3x + -8y) * (-5x + -4y)
(-3x * (-5x + -4y) + -8y * (-5x + -4y)) = 0
((-5x * -3x + -4y * -3x) + -8y * (-5x + -4y)) = 0

Reorder the terms:
((12xy + 15x2) + -8y * (-5x + -4y)) = 0
((12xy + 15x2) + -8y * (-5x + -4y)) = 0
(12xy + 15x2 + (-5x * -8y + -4y * -8y)) = 0
(12xy + 15x2 + (40xy + 32y2)) = 0

Reorder the terms:
(12xy + 40xy + 15x2 + 32y2) = 0

Combine like terms: 12xy + 40xy = 52xy
(52xy + 15x2 + 32y2) = 0

Solving
52xy + 15x2 + 32y2 = 0

Solving for variable 'x'.

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


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

Simplifying
3x + 8y = 0

Solving
3x + 8y = 0

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

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

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

Divide each side by '3'.
x = -2.666666667y

Simplifying
x = -2.666666667y
Solution
x = {-0.8y, -2.666666667y}

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