(12z-10)(8z-3)=

Solution for (12z-10)(8z-3)= equation:

Simplifying
(12z + -10)(8z + -3) = 0

Reorder the terms:
(-10 + 12z)(8z + -3) = 0

Reorder the terms:
(-10 + 12z)(-3 + 8z) = 0

Multiply (-10 + 12z) * (-3 + 8z)
(-10(-3 + 8z) + 12z * (-3 + 8z)) = 0
((-3 * -10 + 8z * -10) + 12z * (-3 + 8z)) = 0
((30 + -80z) + 12z * (-3 + 8z)) = 0
(30 + -80z + (-3 * 12z + 8z * 12z)) = 0
(30 + -80z + (-36z + 96z2)) = 0

Combine like terms: -80z + -36z = -116z
(30 + -116z + 96z2) = 0

Solving
30 + -116z + 96z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -58z + 48z2) = 0

Factor a trinomial.
2((3 + -8z)(5 + -6z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -8z)' equal to zero and attempt to solve:

Simplifying
3 + -8z = 0

Solving
3 + -8z = 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 + -8z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8z = 0 + -3
-8z = 0 + -3

Combine like terms: 0 + -3 = -3
-8z = -3

Divide each side by '-8'.
z = 0.375

Simplifying
z = 0.375
Subproblem 2
Set the factor '(5 + -6z)' equal to zero and attempt to solve:

Simplifying
5 + -6z = 0

Solving
5 + -6z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6z = 0 + -5
-6z = 0 + -5

Combine like terms: 0 + -5 = -5
-6z = -5

Divide each side by '-6'.
z = 0.8333333333

Simplifying
z = 0.8333333333
Solution
z = {0.375, 0.8333333333}