10y^2=-5y

Solution for 10y^2=-5y equation:

Simplifying
10y2 = -5y

Solving
10y2 = -5y

Solving for variable 'y'.

Reorder the terms:
5y + 10y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
5y + 10y2 = 0

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

Ignore the factor 5.
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 + 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}