(x+y^2)(x-5y^2)=0

Solution for (x+y^2)(x-5y^2)=0 equation:

Simplifying
(x + y2)(x + -5y2) = 0

Multiply (x + y2) * (x + -5y2)
(x(x + -5y2) + y2(x + -5y2)) = 0
((x * x + -5y2 * x) + y2(x + -5y2)) = 0

Reorder the terms:
((-5xy2 + x2) + y2(x + -5y2)) = 0
((-5xy2 + x2) + y2(x + -5y2)) = 0
(-5xy2 + x2 + (x * y2 + -5y2 * y2)) = 0
(-5xy2 + x2 + (xy2 + -5y4)) = 0

Reorder the terms:
(-5xy2 + xy2 + x2 + -5y4) = 0

Combine like terms: -5xy2 + xy2 = -4xy2
(-4xy2 + x2 + -5y4) = 0

Solving
-4xy2 + x2 + -5y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -5y2)(x + y2) = 0

Subproblem 1
Set the factor '(x + -5y2)' equal to zero and attempt to solve:

Simplifying
x + -5y2 = 0

Solving
x + -5y2 = 0

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

Add '5y2' to each side of the equation.
x + -5y2 + 5y2 = 0 + 5y2

Combine like terms: -5y2 + 5y2 = 0
x + 0 = 0 + 5y2
x = 0 + 5y2
Remove the zero:
x = 5y2

Simplifying
x = 5y2
Subproblem 2
Set the factor '(x + y2)' equal to zero and attempt to solve:

Simplifying
x + y2 = 0

Solving
x + y2 = 0

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

Add '-1y2' to each side of the equation.
x + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
x + 0 = 0 + -1y2
x = 0 + -1y2
Remove the zero:
x = -1y2

Simplifying
x = -1y2
Solution
x = {5y2, -1y2}