y(2y+3)=0

Solution for y(2y+3)=0 equation:

Simplifying
y(2y + 3) = 0

Reorder the terms:
y(3 + 2y) = 0
(3 * y + 2y * y) = 0
(3y + 2y2) = 0

Solving
3y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(3 + 2y) = 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 '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

Solving
3 + 2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {0, -1.5}