=y-6y^3

Solution for =y-6y^3 equation:

Simplifying
0 = y + -6y3

Solving
0 = y + -6y3

Solving for variable 'y'.
Remove the zero:
-1y + 6y3 = y + -6y3 + -1y + 6y3

Reorder the terms:
-1y + 6y3 = y + -1y + -6y3 + 6y3

Combine like terms: y + -1y = 0
-1y + 6y3 = 0 + -6y3 + 6y3
-1y + 6y3 = -6y3 + 6y3

Combine like terms: -6y3 + 6y3 = 0
-1y + 6y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1 + 6y2) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-1 + 6y2)' equal to zero and attempt to solve:

Simplifying
-1 + 6y2 = 0

Solving
-1 + 6y2 = 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 + 6y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 6y2 = 0 + 1
6y2 = 0 + 1

Combine like terms: 0 + 1 = 1
6y2 = 1

Divide each side by '6'.
y2 = 0.1666666667

Simplifying
y2 = 0.1666666667

Take the square root of each side:
y = {-0.408248291, 0.408248291}
Solution
y = {0, -0.408248291, 0.408248291}