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

Solution for (9-y)(3y-1)=0 equation:

Simplifying
(9 + -1y)(3y + -1) = 0

Reorder the terms:
(9 + -1y)(-1 + 3y) = 0

Multiply (9 + -1y) * (-1 + 3y)
(9(-1 + 3y) + -1y * (-1 + 3y)) = 0
((-1 * 9 + 3y * 9) + -1y * (-1 + 3y)) = 0
((-9 + 27y) + -1y * (-1 + 3y)) = 0
(-9 + 27y + (-1 * -1y + 3y * -1y)) = 0
(-9 + 27y + (1y + -3y2)) = 0

Combine like terms: 27y + 1y = 28y
(-9 + 28y + -3y2) = 0

Solving
-9 + 28y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-9 + y)(1 + -3y) = 0

Subproblem 1
Set the factor '(-9 + y)' equal to zero and attempt to solve:

Simplifying
-9 + y = 0

Solving
-9 + y = 0

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

Add '9' to each side of the equation.
-9 + 9 + y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + y = 0 + 9
y = 0 + 9

Combine like terms: 0 + 9 = 9
y = 9

Simplifying
y = 9
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 = {9, 0.3333333333}