-3y(y-4)(y+6)=0

Solution for -3y(y-4)(y+6)=0 equation:

Simplifying
-3y(y + -4)(y + 6) = 0

Reorder the terms:
-3y(-4 + y)(y + 6) = 0

Reorder the terms:
-3y(-4 + y)(6 + y) = 0

Multiply (-4 + y) * (6 + y)
-3y(-4(6 + y) + y(6 + y)) = 0
-3y((6 * -4 + y * -4) + y(6 + y)) = 0
-3y((-24 + -4y) + y(6 + y)) = 0
-3y(-24 + -4y + (6 * y + y * y)) = 0
-3y(-24 + -4y + (6y + y2)) = 0

Combine like terms: -4y + 6y = 2y
-3y(-24 + 2y + y2) = 0
(-24 * -3y + 2y * -3y + y2 * -3y) = 0
(72y + -6y2 + -3y3) = 0

Solving
72y + -6y2 + -3y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(24 + -2y + -1y2) = 0

Factor a trinomial.
3y((4 + -1y)(6 + y)) = 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 '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Subproblem 3
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Solution
y = {0, 4, -6}