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

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

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

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

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

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

Combine like terms: -1y + 18y = 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}