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

Solution for 4(y+2)(-y-3)=0 equation:

Simplifying
4(y + 2)(-1y + -3) = 0

Reorder the terms:
4(2 + y)(-1y + -3) = 0

Reorder the terms:
4(2 + y)(-3 + -1y) = 0

Multiply (2 + y) * (-3 + -1y)
4(2(-3 + -1y) + y(-3 + -1y)) = 0
4((-3 * 2 + -1y * 2) + y(-3 + -1y)) = 0
4((-6 + -2y) + y(-3 + -1y)) = 0
4(-6 + -2y + (-3 * y + -1y * y)) = 0
4(-6 + -2y + (-3y + -1y2)) = 0

Combine like terms: -2y + -3y = -5y
4(-6 + -5y + -1y2) = 0
(-6 * 4 + -5y * 4 + -1y2 * 4) = 0
(-24 + -20y + -4y2) = 0

Solving
-24 + -20y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(6 + 5y + y2) = 0

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

Ignore the factor -4.
Subproblem 1
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

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

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

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

Simplifying
y = -3
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2
Solution
y = {-3, -2}