5z(z-3)(z+6)=0

Solution for 5z(z-3)(z+6)=0 equation:

Simplifying
5z(z + -3)(z + 6) = 0

Reorder the terms:
5z(-3 + z)(z + 6) = 0

Reorder the terms:
5z(-3 + z)(6 + z) = 0

Multiply (-3 + z) * (6 + z)
5z(-3(6 + z) + z(6 + z)) = 0
5z((6 * -3 + z * -3) + z(6 + z)) = 0
5z((-18 + -3z) + z(6 + z)) = 0
5z(-18 + -3z + (6 * z + z * z)) = 0
5z(-18 + -3z + (6z + z2)) = 0

Combine like terms: -3z + 6z = 3z
5z(-18 + 3z + z2) = 0
(-18 * 5z + 3z * 5z + z2 * 5z) = 0
(-90z + 15z2 + 5z3) = 0

Solving
-90z + 15z2 + 5z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5z'.
5z(-18 + 3z + z2) = 0

Factor a trinomial.
5z((-6 + -1z)(3 + -1z)) = 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 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 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 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

Divide each side by '-1'.
z = -6

Simplifying
z = -6
Subproblem 3
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

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