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

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


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

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

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

Reorder the terms:
(25xy + -4xy + 5x2 + -20y2) = 0

Combine like terms: 25xy + -4xy = 21xy
(21xy + 5x2 + -20y2) = 0

Solving
21xy + 5x2 + -20y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -4y)(x + 5y) = 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 '(x + 5y)' equal to zero and attempt to solve:

Simplifying
x + 5y = 0

Solving
x + 5y = 0

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

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

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

Simplifying
x = -5y
Solution
x = {0.8y, -5y}

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