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

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

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

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

Multiply (-3 + 2z) * (4 + -1z)
(-3(4 + -1z) + 2z * (4 + -1z)) = 0
((4 * -3 + -1z * -3) + 2z * (4 + -1z)) = 0
((-12 + 3z) + 2z * (4 + -1z)) = 0
(-12 + 3z + (4 * 2z + -1z * 2z)) = 0
(-12 + 3z + (8z + -2z2)) = 0

Combine like terms: 3z + 8z = 11z
(-12 + 11z + -2z2) = 0

Solving
-12 + 11z + -2z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(-4 + z)' equal to zero and attempt to solve:

Simplifying
-4 + z = 0

Solving
-4 + z = 0

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

Add '4' to each side of the equation.
-4 + 4 + z = 0 + 4

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

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

Simplifying
z = 4
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 = {4, 1.5}