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

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

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

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

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

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

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

Solving
-24y + -2y2 + y3 = 0

Solving for variable 'y'.

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

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

Simplifying
6 + -1y = 0

Solving
6 + -1y = 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 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

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