(4y+6)(2-y)=0

Solution for (4y+6)(2-y)=0 equation:

Simplifying
(4y + 6)(2 + -1y) = 0

Reorder the terms:
(6 + 4y)(2 + -1y) = 0

Multiply (6 + 4y) * (2 + -1y)
(6(2 + -1y) + 4y * (2 + -1y)) = 0
((2 * 6 + -1y * 6) + 4y * (2 + -1y)) = 0
((12 + -6y) + 4y * (2 + -1y)) = 0
(12 + -6y + (2 * 4y + -1y * 4y)) = 0
(12 + -6y + (8y + -4y2)) = 0

Combine like terms: -6y + 8y = 2y
(12 + 2y + -4y2) = 0

Solving
12 + 2y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + y + -2y2) = 0

Factor a trinomial.
2((2 + -1y)(3 + 2y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
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 = {2, -1.5}