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

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

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

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

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

Solving
-3y + -5y2 + 2y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-3 + -5y + 2y2) = 0

Factor a trinomial.
y((-1 + -2y)(3 + -1y)) = 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 '(-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
Subproblem 3
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {0, -0.5, 3}