5x^2-13xy^5-6y^10=0

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Solution for 5x^2-13xy^5-6y^10=0 equation: 


Simplifying
5x2 + -13xy5 + -6y10 = 0

Reorder the terms:
-13xy5 + 5x2 + -6y10 = 0

Solving
-13xy5 + 5x2 + -6y10 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -3y5)(5x + 2y5) = 0


Subproblem 1
Set the factor '(x + -3y5)' equal to zero and attempt to solve:

Simplifying
x + -3y5 = 0

Solving
x + -3y5 = 0

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

Add '3y5' to each side of the equation.
x + -3y5 + 3y5 = 0 + 3y5

Combine like terms: -3y5 + 3y5 = 0
x + 0 = 0 + 3y5
x = 0 + 3y5
Remove the zero:
x = 3y5

Simplifying
x = 3y5

Subproblem 2
Set the factor '(5x + 2y5)' equal to zero and attempt to solve:

Simplifying
5x + 2y5 = 0

Solving
5x + 2y5 = 0

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

Add '-2y5' to each side of the equation.
5x + 2y5 + -2y5 = 0 + -2y5

Combine like terms: 2y5 + -2y5 = 0
5x + 0 = 0 + -2y5
5x = 0 + -2y5
Remove the zero:
5x = -2y5

Divide each side by '5'.
x = -0.4y5

Simplifying
x = -0.4y5
Solution
x = {3y5, -0.4y5}

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