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

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

Simplifying
(4z + 5)(6 + -1z) = 0

Reorder the terms:
(5 + 4z)(6 + -1z) = 0

Multiply (5 + 4z) * (6 + -1z)
(5(6 + -1z) + 4z * (6 + -1z)) = 0
((6 * 5 + -1z * 5) + 4z * (6 + -1z)) = 0
((30 + -5z) + 4z * (6 + -1z)) = 0
(30 + -5z + (6 * 4z + -1z * 4z)) = 0
(30 + -5z + (24z + -4z2)) = 0

Combine like terms: -5z + 24z = 19z
(30 + 19z + -4z2) = 0

Solving
30 + 19z + -4z2 = 0

Solving for variable 'z'.

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

Subproblem 1
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
Subproblem 2
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
Solution
z = {6, -1.25}