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

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

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

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

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

Combine like terms: 12y + -3y = 9y
(-18 + 9y + 2y2) = 0

Solving
-18 + 9y + 2y2 = 0

Solving for variable 'y'.

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

Simplifying
3 + -2y = 0

Solving
3 + -2y = 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 + -2y = 0 + -3

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

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

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-6, 1.5}