(4Y+6)(3-Y)=0

Solution for (4Y+6)(3-Y)=0 equation:

Simplifying
(4Y + 6)(3 + -1Y) = 0

Reorder the terms:
(6 + 4Y)(3 + -1Y) = 0

Multiply (6 + 4Y) * (3 + -1Y)
(6(3 + -1Y) + 4Y * (3 + -1Y)) = 0
((3 * 6 + -1Y * 6) + 4Y * (3 + -1Y)) = 0
((18 + -6Y) + 4Y * (3 + -1Y)) = 0
(18 + -6Y + (3 * 4Y + -1Y * 4Y)) = 0
(18 + -6Y + (12Y + -4Y2)) = 0

Combine like terms: -6Y + 12Y = 6Y
(18 + 6Y + -4Y2) = 0

Solving
18 + 6Y + -4Y2 = 0

Solving for variable 'Y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 3Y + -2Y2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1Y)' equal to zero and attempt to solve:

Simplifying
3 + -1Y = 0

Solving
3 + -1Y = 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 + -1Y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1Y = 0 + -3
-1Y = 0 + -3

Combine like terms: 0 + -3 = -3
-1Y = -3

Divide each side by '-1'.
Y = 3

Simplifying
Y = 3
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 = {3, -1.5}