(2z-8)*(3z+6)=0

Solution for (2z-8)*(3z+6)=0 equation:

Simplifying
(2z + -8)(3z + 6) = 0

Reorder the terms:
(-8 + 2z)(3z + 6) = 0

Reorder the terms:
(-8 + 2z)(6 + 3z) = 0

Multiply (-8 + 2z) * (6 + 3z)
(-8(6 + 3z) + 2z * (6 + 3z)) = 0
((6 * -8 + 3z * -8) + 2z * (6 + 3z)) = 0
((-48 + -24z) + 2z * (6 + 3z)) = 0
(-48 + -24z + (6 * 2z + 3z * 2z)) = 0
(-48 + -24z + (12z + 6z2)) = 0

Combine like terms: -24z + 12z = -12z
(-48 + -12z + 6z2) = 0

Solving
-48 + -12z + 6z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + -2z + z2) = 0

Factor a trinomial.
6((-2 + -1z)(4 + -1z)) = 0

Ignore the factor 6.
Subproblem 1
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 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {-2, 4}