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

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

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

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

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

Combine like terms: -1y + 9y = 8y
(3 + 8y + -3y2) = 0

Solving
3 + 8y + -3y2 = 0

Solving for variable 'y'.

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

Subproblem 1
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 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 = {3, -0.3333333333}