(1-y)(3-y)(6-y)=18

Solution for (1-y)(3-y)(6-y)=18 equation:

Simplifying
(1 + -1y)(3 + -1y)(6 + -1y) = 18

Multiply (1 + -1y) * (3 + -1y)
(1(3 + -1y) + -1y * (3 + -1y))(6 + -1y) = 18
((3 * 1 + -1y * 1) + -1y * (3 + -1y))(6 + -1y) = 18
((3 + -1y) + -1y * (3 + -1y))(6 + -1y) = 18
(3 + -1y + (3 * -1y + -1y * -1y))(6 + -1y) = 18
(3 + -1y + (-3y + 1y2))(6 + -1y) = 18

Combine like terms: -1y + -3y = -4y
(3 + -4y + 1y2)(6 + -1y) = 18

Multiply (3 + -4y + 1y2) * (6 + -1y)
(3(6 + -1y) + -4y * (6 + -1y) + 1y2 * (6 + -1y)) = 18
((6 * 3 + -1y * 3) + -4y * (6 + -1y) + 1y2 * (6 + -1y)) = 18
((18 + -3y) + -4y * (6 + -1y) + 1y2 * (6 + -1y)) = 18
(18 + -3y + (6 * -4y + -1y * -4y) + 1y2 * (6 + -1y)) = 18
(18 + -3y + (-24y + 4y2) + 1y2 * (6 + -1y)) = 18
(18 + -3y + -24y + 4y2 + (6 * 1y2 + -1y * 1y2)) = 18
(18 + -3y + -24y + 4y2 + (6y2 + -1y3)) = 18

Combine like terms: -3y + -24y = -27y
(18 + -27y + 4y2 + 6y2 + -1y3) = 18

Combine like terms: 4y2 + 6y2 = 10y2
(18 + -27y + 10y2 + -1y3) = 18

Add '-18' to each side of the equation.
18 + -27y + 10y2 + -18 + -1y3 = 18 + -18

Reorder the terms:
18 + -18 + -27y + 10y2 + -1y3 = 18 + -18

Combine like terms: 18 + -18 = 0
0 + -27y + 10y2 + -1y3 = 18 + -18
-27y + 10y2 + -1y3 = 18 + -18

Combine like terms: 18 + -18 = 0
-27y + 10y2 + -1y3 = 0

Solving
-27y + 10y2 + -1y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-27 + 10y + -1y2) = 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 '(-27 + 10y + -1y2)' equal to zero and attempt to solve:

Simplifying
-27 + 10y + -1y2 = 0

Solving
-27 + 10y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
27 + -10y + y2 = 0

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -10y + -27 + y2 = 0 + -27

Reorder the terms:
27 + -27 + -10y + y2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -10y + y2 = 0 + -27
-10y + y2 = 0 + -27

Combine like terms: 0 + -27 = -27
-10y + y2 = -27

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = -27 + 25

Reorder the terms:
25 + -10y + y2 = -27 + 25

Combine like terms: -27 + 25 = -2
25 + -10y + y2 = -2

Factor a perfect square on the left side:
(y + -5)(y + -5) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}