-4z(z+6)(z-2)=0

Solution for -4z(z+6)(z-2)=0 equation:

Simplifying
-4z(z + 6)(z + -2) = 0

Reorder the terms:
-4z(6 + z)(z + -2) = 0

Reorder the terms:
-4z(6 + z)(-2 + z) = 0

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

Combine like terms: 6z + -2z = 4z
-4z(-12 + 4z + z2) = 0
(-12 * -4z + 4z * -4z + z2 * -4z) = 0
(48z + -16z2 + -4z3) = 0

Solving
48z + -16z2 + -4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(12 + -4z + -1z2) = 0

Factor a trinomial.
4z((2 + -1z)(6 + 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 '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
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, 2, -6}