(y+3)(y)(2y+1)=0

Solution for (y+3)(y)(2y+1)=0 equation:

Simplifying
(y + 3)(y)(2y + 1) = 0

Reorder the terms:
(3 + y)(y)(2y + 1) = 0

Reorder the terms:
(3 + y) * y(1 + 2y) = 0

Reorder the terms for easier multiplication:
y(3 + y)(1 + 2y) = 0

Multiply (3 + y) * (1 + 2y)
y(3(1 + 2y) + y(1 + 2y)) = 0
y((1 * 3 + 2y * 3) + y(1 + 2y)) = 0
y((3 + 6y) + y(1 + 2y)) = 0
y(3 + 6y + (1 * y + 2y * y)) = 0
y(3 + 6y + (1y + 2y2)) = 0

Combine like terms: 6y + 1y = 7y
y(3 + 7y + 2y2) = 0
(3 * y + 7y * y + 2y2 * y) = 0
(3y + 7y2 + 2y3) = 0

Solving
3y + 7y2 + 2y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(3 + 7y + 2y2) = 0

Factor a trinomial.
y((3 + y)(1 + 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 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

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

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

Simplifying
y = -3
Subproblem 3
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, -3, -0.5}