-5z(z+6)(z+5)=0

Solution for -5z(z+6)(z+5)=0 equation:

Simplifying
-5z(z + 6)(z + 5) = 0

Reorder the terms:
-5z(6 + z)(z + 5) = 0

Reorder the terms:
-5z(6 + z)(5 + z) = 0

Multiply (6 + z) * (5 + z)
-5z(6(5 + z) + z(5 + z)) = 0
-5z((5 * 6 + z * 6) + z(5 + z)) = 0
-5z((30 + 6z) + z(5 + z)) = 0
-5z(30 + 6z + (5 * z + z * z)) = 0
-5z(30 + 6z + (5z + z2)) = 0

Combine like terms: 6z + 5z = 11z
-5z(30 + 11z + z2) = 0
(30 * -5z + 11z * -5z + z2 * -5z) = 0
(-150z + -55z2 + -5z3) = 0

Solving
-150z + -55z2 + -5z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '-5z'.
-5z(30 + 11z + z2) = 0

Factor a trinomial.
-5z((6 + z)(5 + z)) = 0

Ignore the factor -5.
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 '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 0

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

Add '-6' to each side of the equation.
6 + -6 + z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + z = 0 + -6
z = 0 + -6

Combine like terms: 0 + -6 = -6
z = -6

Simplifying
z = -6
Subproblem 3
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
Solution
z = {0, -6, -5}