(8z-6)(12z+4)=0

Solution for (8z-6)(12z+4)=0 equation:

Simplifying
(8z + -6)(12z + 4) = 0

Reorder the terms:
(-6 + 8z)(12z + 4) = 0

Reorder the terms:
(-6 + 8z)(4 + 12z) = 0

Multiply (-6 + 8z) * (4 + 12z)
(-6(4 + 12z) + 8z * (4 + 12z)) = 0
((4 * -6 + 12z * -6) + 8z * (4 + 12z)) = 0
((-24 + -72z) + 8z * (4 + 12z)) = 0
(-24 + -72z + (4 * 8z + 12z * 8z)) = 0
(-24 + -72z + (32z + 96z2)) = 0

Combine like terms: -72z + 32z = -40z
(-24 + -40z + 96z2) = 0

Solving
-24 + -40z + 96z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-3 + -5z + 12z2) = 0

Factor a trinomial.
8((-1 + -3z)(3 + -4z)) = 0

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

Simplifying
-1 + -3z = 0

Solving
-1 + -3z = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3z = 0 + 1

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

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

Divide each side by '-3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 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 + -4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4z = 0 + -3
-4z = 0 + -3

Combine like terms: 0 + -3 = -3
-4z = -3

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Solution
z = {-0.3333333333, 0.75}