(2z-1)(4z-3)=0

Solution for (2z-1)(4z-3)=0 equation:

Simplifying
(2z + -1)(4z + -3) = 0

Reorder the terms:
(-1 + 2z)(4z + -3) = 0

Reorder the terms:
(-1 + 2z)(-3 + 4z) = 0

Multiply (-1 + 2z) * (-3 + 4z)
(-1(-3 + 4z) + 2z * (-3 + 4z)) = 0
((-3 * -1 + 4z * -1) + 2z * (-3 + 4z)) = 0
((3 + -4z) + 2z * (-3 + 4z)) = 0
(3 + -4z + (-3 * 2z + 4z * 2z)) = 0
(3 + -4z + (-6z + 8z2)) = 0

Combine like terms: -4z + -6z = -10z
(3 + -10z + 8z2) = 0

Solving
3 + -10z + 8z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -2z)(3 + -4z) = 0

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

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
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 = {0.5, 0.75}