(8z-3)(2z-3)=0

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

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

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

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

Multiply (-3 + 8z) * (-3 + 2z)
(-3(-3 + 2z) + 8z * (-3 + 2z)) = 0
((-3 * -3 + 2z * -3) + 8z * (-3 + 2z)) = 0
((9 + -6z) + 8z * (-3 + 2z)) = 0
(9 + -6z + (-3 * 8z + 2z * 8z)) = 0
(9 + -6z + (-24z + 16z2)) = 0

Combine like terms: -6z + -24z = -30z
(9 + -30z + 16z2) = 0

Solving
9 + -30z + 16z2 = 0

Solving for variable 'z'.

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

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 '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 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 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {0.375, 1.5}