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

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

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

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

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

Multiply (-3 + y) * (-6 + y)
4y(-3(-6 + y) + y(-6 + y)) = 0
4y((-6 * -3 + y * -3) + y(-6 + y)) = 0
4y((18 + -3y) + y(-6 + y)) = 0
4y(18 + -3y + (-6 * y + y * y)) = 0
4y(18 + -3y + (-6y + y2)) = 0

Combine like terms: -3y + -6y = -9y
4y(18 + -9y + y2) = 0
(18 * 4y + -9y * 4y + y2 * 4y) = 0
(72y + -36y2 + 4y3) = 0

Solving
72y + -36y2 + 4y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(18 + -9y + y2) = 0

Factor a trinomial.
4y((3 + -1y)(6 + -1y)) = 0

Ignore the factor 4.
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 + -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
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, 3, 6}