(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 = 17y
(6 + 17y + -3y2) = 0

Solving
6 + 17y + -3y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 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 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
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}