3z(z-1)(z+6)=0

Solution for 3z(z-1)(z+6)=0 equation:

Simplifying
3z(z + -1)(z + 6) = 0

Reorder the terms:
3z(-1 + z)(z + 6) = 0

Reorder the terms:
3z(-1 + z)(6 + z) = 0

Multiply (-1 + z) * (6 + z)
3z(-1(6 + z) + z(6 + z)) = 0
3z((6 * -1 + z * -1) + z(6 + z)) = 0
3z((-6 + -1z) + z(6 + z)) = 0
3z(-6 + -1z + (6 * z + z * z)) = 0
3z(-6 + -1z + (6z + z2)) = 0

Combine like terms: -1z + 6z = 5z
3z(-6 + 5z + z2) = 0
(-6 * 3z + 5z * 3z + z2 * 3z) = 0
(-18z + 15z2 + 3z3) = 0

Solving
-18z + 15z2 + 3z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(-6 + 5z + z2) = 0

Factor a trinomial.
3z((-6 + -1z)(1 + -1z)) = 0

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

Simplifying
1 + -1z = 0

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

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

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

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

Simplifying
z = 1
Solution
z = {0, -6, 1}