8y^3+2y-3y=0

Solution for 8y^3+2y-3y=0 equation:

Simplifying
8y3 + 2y + -3y = 0

Reorder the terms:
2y + -3y + 8y3 = 0

Combine like terms: 2y + -3y = -1y
-1y + 8y3 = 0

Solving
-1y + 8y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1 + 8y2) = 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 + 8y2)' equal to zero and attempt to solve:

Simplifying
-1 + 8y2 = 0

Solving
-1 + 8y2 = 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 + 8y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8y2 = 0 + 1
8y2 = 0 + 1

Combine like terms: 0 + 1 = 1
8y2 = 1

Divide each side by '8'.
y2 = 0.125

Simplifying
y2 = 0.125

Take the square root of each side:
y = {-0.353553391, 0.353553391}
Solution
y = {0, -0.353553391, 0.353553391}