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

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


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

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

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

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

Combine like terms: xy + -25xy = -24xy
(-24xy + 5x2 + -5y2) = 0

Solving
-24xy + 5x2 + -5y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(5x + y)' equal to zero and attempt to solve:

Simplifying
5x + y = 0

Solving
5x + y = 0

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

Add '-1y' to each side of the equation.
5x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
5x + 0 = 0 + -1y
5x = 0 + -1y
Remove the zero:
5x = -1y

Divide each side by '5'.
x = -0.2y

Simplifying
x = -0.2y
Solution
x = {5y, -0.2y}

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