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

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

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

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

Multiply (6 + 4y) * (4 + -1y)
(6(4 + -1y) + 4y * (4 + -1y)) = 0
((4 * 6 + -1y * 6) + 4y * (4 + -1y)) = 0
((24 + -6y) + 4y * (4 + -1y)) = 0
(24 + -6y + (4 * 4y + -1y * 4y)) = 0
(24 + -6y + (16y + -4y2)) = 0

Combine like terms: -6y + 16y = 10y
(24 + 10y + -4y2) = 0

Solving
24 + 10y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 5y + -2y2) = 0

Factor a trinomial.
2((4 + -1y)(3 + 2y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
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 = {4, -1.5}