(4z-3)(6-z)=0

Solution for (4z-3)(6-z)=0 equation:

Simplifying
(4z + -3)(6 + -1z) = 0

Reorder the terms:
(-3 + 4z)(6 + -1z) = 0

Multiply (-3 + 4z) * (6 + -1z)
(-3(6 + -1z) + 4z * (6 + -1z)) = 0
((6 * -3 + -1z * -3) + 4z * (6 + -1z)) = 0
((-18 + 3z) + 4z * (6 + -1z)) = 0
(-18 + 3z + (6 * 4z + -1z * 4z)) = 0
(-18 + 3z + (24z + -4z2)) = 0

Combine like terms: 3z + 24z = 27z
(-18 + 27z + -4z2) = 0

Solving
-18 + 27z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + z)(3 + -4z) = 0

Subproblem 1
Set the factor '(-6 + z)' equal to zero and attempt to solve:

Simplifying
-6 + z = 0

Solving
-6 + z = 0

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

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

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

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

Simplifying
z = 6
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 = {6, 0.75}