z(z+6)(z-6)=

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

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

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

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

Multiply (6 + z) * (-6 + z)
z(6(-6 + z) + z(-6 + z)) = 0
z((-6 * 6 + z * 6) + z(-6 + z)) = 0
z((-36 + 6z) + z(-6 + z)) = 0
z(-36 + 6z + (-6 * z + z * z)) = 0
z(-36 + 6z + (-6z + z2)) = 0

Combine like terms: 6z + -6z = 0
z(-36 + 0 + z2) = 0
z(-36 + z2) = 0
(-36 * z + z2 * z) = 0
(-36z + z3) = 0

Solving
-36z + z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-36 + z2) = 0

Factor a difference between two squares.
z((6 + z)(-6 + z)) = 0

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 '(-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
Solution
z = {0, -6, 6}