(3z-5)(4-z)=0

Solution for (3z-5)(4-z)=0 equation:

Simplifying
(3z + -5)(4 + -1z) = 0

Reorder the terms:
(-5 + 3z)(4 + -1z) = 0

Multiply (-5 + 3z) * (4 + -1z)
(-5(4 + -1z) + 3z * (4 + -1z)) = 0
((4 * -5 + -1z * -5) + 3z * (4 + -1z)) = 0
((-20 + 5z) + 3z * (4 + -1z)) = 0
(-20 + 5z + (4 * 3z + -1z * 3z)) = 0
(-20 + 5z + (12z + -3z2)) = 0

Combine like terms: 5z + 12z = 17z
(-20 + 17z + -3z2) = 0

Solving
-20 + 17z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-4 + z)(5 + -3z) = 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 '(5 + -3z)' equal to zero and attempt to solve:

Simplifying
5 + -3z = 0

Solving
5 + -3z = 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 + -3z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3z = 0 + -5
-3z = 0 + -5

Combine like terms: 0 + -5 = -5
-3z = -5

Divide each side by '-3'.
z = 1.666666667

Simplifying
z = 1.666666667
Solution
z = {4, 1.666666667}