6x^4y-3750y^5=0

Solution for 6x^4y-3750y^5=0 equation:

Simplifying
6x4y + -3750y5 = 0

Solving
6x4y + -3750y5 = 0

Solving for variable 'x'.

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

Add '3750y5' to each side of the equation.
6x4y + -3750y5 + 3750y5 = 0 + 3750y5

Combine like terms: -3750y5 + 3750y5 = 0
6x4y + 0 = 0 + 3750y5
6x4y = 0 + 3750y5
Remove the zero:
6x4y = 3750y5

Divide each side by '6y'.
x4 = 625y4

Simplifying
x4 = 625y4

Combine like terms: 625y4 + -625y4 = 0
x4 + -625y4 = 0

Factor a difference between two squares.
(x2 + 25y2)(x2 + -25y2) = 0

Factor a difference between two squares.
(x2 + 25y2)((x + 5y)(x + -5y)) = 0

Subproblem 1
Set the factor '(x2 + 25y2)' equal to zero and attempt to solve:

Simplifying
x2 + 25y2 = 0

Solving
x2 + 25y2 = 0

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

Add '-25y2' to each side of the equation.
x2 + 25y2 + -25y2 = 0 + -25y2

Combine like terms: 25y2 + -25y2 = 0
x2 + 0 = 0 + -25y2
x2 = 0 + -25y2
Remove the zero:
x2 = -25y2

Simplifying
x2 = -25y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
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 3
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
Solution
x = {-5y, 5y}