4y(y-3)(y-2)=0

Solution for 4y(y-3)(y-2)=0 equation:

Simplifying
4y(y + -3)(y + -2) = 0

Reorder the terms:
4y(-3 + y)(y + -2) = 0

Reorder the terms:
4y(-3 + y)(-2 + y) = 0

Multiply (-3 + y) * (-2 + y)
4y(-3(-2 + y) + y(-2 + y)) = 0
4y((-2 * -3 + y * -3) + y(-2 + y)) = 0
4y((6 + -3y) + y(-2 + y)) = 0
4y(6 + -3y + (-2 * y + y * y)) = 0
4y(6 + -3y + (-2y + y2)) = 0

Combine like terms: -3y + -2y = -5y
4y(6 + -5y + y2) = 0
(6 * 4y + -5y * 4y + y2 * 4y) = 0
(24y + -20y2 + 4y3) = 0

Solving
24y + -20y2 + 4y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(6 + -5y + y2) = 0

Factor a trinomial.
4y((2 + -1y)(3 + -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 '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
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, 2, 3}