-4z(z+1)(z+4)=0

Solution for -4z(z+1)(z+4)=0 equation:

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

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

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

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

Combine like terms: 1z + 4z = 5z
-4z(4 + 5z + z2) = 0
(4 * -4z + 5z * -4z + z2 * -4z) = 0
(-16z + -20z2 + -4z3) = 0

Solving
-16z + -20z2 + -4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '-4z'.
-4z(4 + 5z + z2) = 0

Factor a trinomial.
-4z((4 + z)(1 + z)) = 0

Ignore the factor -4.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
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
Subproblem 3
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

Combine like terms: 1 + -1 = 0
0 + z = 0 + -1
z = 0 + -1

Combine like terms: 0 + -1 = -1
z = -1

Simplifying
z = -1
Solution
z = {0, -4, -1}