(6-y)(3y-1)=0

Solution for (6-y)(3y-1)=0 equation:

Simplifying
(6 + -1y)(3y + -1) = 0

Reorder the terms:
(6 + -1y)(-1 + 3y) = 0

Multiply (6 + -1y) * (-1 + 3y)
(6(-1 + 3y) + -1y * (-1 + 3y)) = 0
((-1 * 6 + 3y * 6) + -1y * (-1 + 3y)) = 0
((-6 + 18y) + -1y * (-1 + 3y)) = 0
(-6 + 18y + (-1 * -1y + 3y * -1y)) = 0
(-6 + 18y + (1y + -3y2)) = 0

Combine like terms: 18y + 1y = 19y
(-6 + 19y + -3y2) = 0

Solving
-6 + 19y + -3y2 = 0

Solving for variable 'y'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -3y)' equal to zero and attempt to solve:

Simplifying
1 + -3y = 0

Solving
1 + -3y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3y = 0 + -1
-3y = 0 + -1

Combine like terms: 0 + -1 = -1
-3y = -1

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Solution
y = {6, 0.3333333333}