16x^2-80xy+100y^2=0

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Solution for 16x^2-80xy+100y^2=0 equation: 


Simplifying
16x2 + -80xy + 100y2 = 0

Reorder the terms:
-80xy + 16x2 + 100y2 = 0

Solving
-80xy + 16x2 + 100y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-20xy + 4x2 + 25y2) = 0

Factor a trinomial.
4((2x + -5y)(2x + -5y)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2x + -5y)' equal to zero and attempt to solve:

Simplifying
2x + -5y = 0

Solving
2x + -5y = 0

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

Add '5y' to each side of the equation.
2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
2x + 0 = 0 + 5y
2x = 0 + 5y
Remove the zero:
2x = 5y

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y

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

Simplifying
2x + -5y = 0

Solving
2x + -5y = 0

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

Add '5y' to each side of the equation.
2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
2x + 0 = 0 + 5y
2x = 0 + 5y
Remove the zero:
2x = 5y

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y
Solution
x = {2.5y, 2.5y}

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