(4z-8)(2z+6)=0

Solution for (4z-8)(2z+6)=0 equation:

Simplifying
(4z + -8)(2z + 6) = 0

Reorder the terms:
(-8 + 4z)(2z + 6) = 0

Reorder the terms:
(-8 + 4z)(6 + 2z) = 0

Multiply (-8 + 4z) * (6 + 2z)
(-8(6 + 2z) + 4z * (6 + 2z)) = 0
((6 * -8 + 2z * -8) + 4z * (6 + 2z)) = 0
((-48 + -16z) + 4z * (6 + 2z)) = 0
(-48 + -16z + (6 * 4z + 2z * 4z)) = 0
(-48 + -16z + (24z + 8z2)) = 0

Combine like terms: -16z + 24z = 8z
(-48 + 8z + 8z2) = 0

Solving
-48 + 8z + 8z2 = 0

Solving for variable 'z'.

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

Factor a trinomial.
8((-3 + -1z)(2 + -1z)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 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 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
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
Solution
z = {-3, 2}