(4z-5)(z-6)=0

Solution for (4z-5)(z-6)=0 equation:

Simplifying
(4z + -5)(z + -6) = 0

Reorder the terms:
(-5 + 4z)(z + -6) = 0

Reorder the terms:
(-5 + 4z)(-6 + z) = 0

Multiply (-5 + 4z) * (-6 + z)
(-5(-6 + z) + 4z * (-6 + z)) = 0
((-6 * -5 + z * -5) + 4z * (-6 + z)) = 0
((30 + -5z) + 4z * (-6 + z)) = 0
(30 + -5z + (-6 * 4z + z * 4z)) = 0
(30 + -5z + (-24z + 4z2)) = 0

Combine like terms: -5z + -24z = -29z
(30 + -29z + 4z2) = 0

Solving
30 + -29z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + -4z)(6 + -1z) = 0

Subproblem 1
Set the factor '(5 + -4z)' equal to zero and attempt to solve:

Simplifying
5 + -4z = 0

Solving
5 + -4z = 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 + -4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4z = 0 + -5
-4z = 0 + -5

Combine like terms: 0 + -5 = -5
-4z = -5

Divide each side by '-4'.
z = 1.25

Simplifying
z = 1.25
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 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 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {1.25, 6}