10y^3+5y^2=0

Solution for 10y^3+5y^2=0 equation:

Simplifying
10y3 + 5y2 = 0

Reorder the terms:
5y2 + 10y3 = 0

Solving
5y2 + 10y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y2'.
5y2(1 + 2y) = 0

Ignore the factor 5.
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 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {0, -0.5}