4y(10y^3+2y)=

Solution for 4y(10y^3+2y)= equation:

Simplifying
4y(10y3 + 2y) = 0

Reorder the terms:
4y(2y + 10y3) = 0
(2y * 4y + 10y3 * 4y) = 0
(8y2 + 40y4) = 0

Solving
8y2 + 40y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '8y2'.
8y2(1 + 5y2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(1 + 5y2)' equal to zero and attempt to solve:

Simplifying
1 + 5y2 = 0

Solving
1 + 5y2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5y2 = 0 + -1
5y2 = 0 + -1

Combine like terms: 0 + -1 = -1
5y2 = -1

Divide each side by '5'.
y2 = -0.2

Simplifying
y2 = -0.2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}