(-4y-5x)(5y+3x)=

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


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

Reorder the terms:
(-5x + -4y)(5y + 3x) = 0

Reorder the terms:
(-5x + -4y)(3x + 5y) = 0

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

Reorder the terms:
((-25xy + -15x2) + -4y * (3x + 5y)) = 0
((-25xy + -15x2) + -4y * (3x + 5y)) = 0
(-25xy + -15x2 + (3x * -4y + 5y * -4y)) = 0
(-25xy + -15x2 + (-12xy + -20y2)) = 0

Reorder the terms:
(-25xy + -12xy + -15x2 + -20y2) = 0

Combine like terms: -25xy + -12xy = -37xy
(-37xy + -15x2 + -20y2) = 0

Solving
-37xy + -15x2 + -20y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(37xy + 15x2 + 20y2) = 0

Factor a trinomial.
-1((5x + 4y)(3x + 5y)) = 0

Ignore the factor -1.

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 + 5y)' equal to zero and attempt to solve:

Simplifying
3x + 5y = 0

Solving
3x + 5y = 0

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

Add '-5y' to each side of the equation.
3x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
3x + 0 = 0 + -5y
3x = 0 + -5y
Remove the zero:
3x = -5y

Divide each side by '3'.
x = -1.666666667y

Simplifying
x = -1.666666667y
Solution
x = {-0.8y, -1.666666667y}

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