(2z+6)(2z-6)z=

Solution for (2z+6)(2z-6)z= equation:

Simplifying
(2z + 6)(2z + -6) * z = 0

Reorder the terms:
(6 + 2z)(2z + -6) * z = 0

Reorder the terms:
(6 + 2z)(-6 + 2z) * z = 0

Reorder the terms for easier multiplication:
z(6 + 2z)(-6 + 2z) = 0

Multiply (6 + 2z) * (-6 + 2z)
z(6(-6 + 2z) + 2z * (-6 + 2z)) = 0
z((-6 * 6 + 2z * 6) + 2z * (-6 + 2z)) = 0
z((-36 + 12z) + 2z * (-6 + 2z)) = 0
z(-36 + 12z + (-6 * 2z + 2z * 2z)) = 0
z(-36 + 12z + (-12z + 4z2)) = 0

Combine like terms: 12z + -12z = 0
z(-36 + 0 + 4z2) = 0
z(-36 + 4z2) = 0
(-36 * z + 4z2 * z) = 0
(-36z + 4z3) = 0

Solving
-36z + 4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(-9 + z2) = 0

Factor a difference between two squares.
4z((3 + z)(-3 + 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 '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 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 + z = 0 + -3

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

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

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

Simplifying
-3 + z = 0

Solving
-3 + z = 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 + z = 0 + 3

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

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

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