5y^3+2y(3y^2-2)=

Solution for 5y^3+2y(3y^2-2)= equation:

Simplifying
5y3 + 2y(3y2 + -2) = 0

Reorder the terms:
5y3 + 2y(-2 + 3y2) = 0
5y3 + (-2 * 2y + 3y2 * 2y) = 0
5y3 + (-4y + 6y3) = 0

Reorder the terms:
-4y + 5y3 + 6y3 = 0

Combine like terms: 5y3 + 6y3 = 11y3
-4y + 11y3 = 0

Solving
-4y + 11y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-4 + 11y2) = 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 '(-4 + 11y2)' equal to zero and attempt to solve:

Simplifying
-4 + 11y2 = 0

Solving
-4 + 11y2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + 11y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 11y2 = 0 + 4
11y2 = 0 + 4

Combine like terms: 0 + 4 = 4
11y2 = 4

Divide each side by '11'.
y2 = 0.3636363636

Simplifying
y2 = 0.3636363636

Take the square root of each side:
y = {-0.603022689, 0.603022689}
Solution
y = {0, -0.603022689, 0.603022689}