3(z+5)(-z-4)=0

Solution for 3(z+5)(-z-4)=0 equation:

Simplifying
3(z + 5)(-1z + -4) = 0

Reorder the terms:
3(5 + z)(-1z + -4) = 0

Reorder the terms:
3(5 + z)(-4 + -1z) = 0

Multiply (5 + z) * (-4 + -1z)
3(5(-4 + -1z) + z(-4 + -1z)) = 0
3((-4 * 5 + -1z * 5) + z(-4 + -1z)) = 0
3((-20 + -5z) + z(-4 + -1z)) = 0
3(-20 + -5z + (-4 * z + -1z * z)) = 0
3(-20 + -5z + (-4z + -1z2)) = 0

Combine like terms: -5z + -4z = -9z
3(-20 + -9z + -1z2) = 0
(-20 * 3 + -9z * 3 + -1z2 * 3) = 0
(-60 + -27z + -3z2) = 0

Solving
-60 + -27z + -3z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(20 + 9z + z2) = 0

Factor a trinomial.
-3((5 + z)(4 + z)) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
Subproblem 2
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

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

Combine like terms: 4 + -4 = 0
0 + z = 0 + -4
z = 0 + -4

Combine like terms: 0 + -4 = -4
z = -4

Simplifying
z = -4
Solution
z = {-5, -4}