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

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

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

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

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

Multiply (1 + y) * (-3 + y)
3y(1(-3 + y) + y(-3 + y)) = 0
3y((-3 * 1 + y * 1) + y(-3 + y)) = 0
3y((-3 + 1y) + y(-3 + y)) = 0
3y(-3 + 1y + (-3 * y + y * y)) = 0
3y(-3 + 1y + (-3y + y2)) = 0

Combine like terms: 1y + -3y = -2y
3y(-3 + -2y + y2) = 0
(-3 * 3y + -2y * 3y + y2 * 3y) = 0
(-9y + -6y2 + 3y3) = 0

Solving
-9y + -6y2 + 3y3 = 0

Solving for variable 'y'.

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

Factor a trinomial.
3y((-1 + -1y)(3 + -1y)) = 0

Ignore the factor 3.
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 + -1y)' equal to zero and attempt to solve:

Simplifying
-1 + -1y = 0

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

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

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

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

Simplifying
y = -1
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, -1, 3}