(3y-2)(6+y)=0

Solution for (3y-2)(6+y)=0 equation:

Simplifying
(3y + -2)(6 + y) = 0

Reorder the terms:
(-2 + 3y)(6 + y) = 0

Multiply (-2 + 3y) * (6 + y)
(-2(6 + y) + 3y * (6 + y)) = 0
((6 * -2 + y * -2) + 3y * (6 + y)) = 0
((-12 + -2y) + 3y * (6 + y)) = 0
(-12 + -2y + (6 * 3y + y * 3y)) = 0
(-12 + -2y + (18y + 3y2)) = 0

Combine like terms: -2y + 18y = 16y
(-12 + 16y + 3y2) = 0

Solving
-12 + 16y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + -1y)(2 + -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 '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3y = 0 + -2
-3y = 0 + -2

Combine like terms: 0 + -2 = -2
-3y = -2

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {-6, 0.6666666667}