4x^2-16xy-20y^2=0

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Solution for 4x^2-16xy-20y^2=0 equation: 


Simplifying
4x2 + -16xy + -20y2 = 0

Reorder the terms:
-16xy + 4x2 + -20y2 = 0

Solving
-16xy + 4x2 + -20y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4xy + x2 + -5y2) = 0

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

Ignore the factor 4.

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {5y, -1y}

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