(5z-6)*(8-z)=0

Solution for (5z-6)*(8-z)=0 equation:

Simplifying
(5z + -6)(8 + -1z) = 0

Reorder the terms:
(-6 + 5z)(8 + -1z) = 0

Multiply (-6 + 5z) * (8 + -1z)
(-6(8 + -1z) + 5z * (8 + -1z)) = 0
((8 * -6 + -1z * -6) + 5z * (8 + -1z)) = 0
((-48 + 6z) + 5z * (8 + -1z)) = 0
(-48 + 6z + (8 * 5z + -1z * 5z)) = 0
(-48 + 6z + (40z + -5z2)) = 0

Combine like terms: 6z + 40z = 46z
(-48 + 46z + -5z2) = 0

Solving
-48 + 46z + -5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + z)(6 + -5z) = 0

Subproblem 1
Set the factor '(-8 + z)' equal to zero and attempt to solve:

Simplifying
-8 + z = 0

Solving
-8 + z = 0

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

Add '8' to each side of the equation.
-8 + 8 + z = 0 + 8

Combine like terms: -8 + 8 = 0
0 + z = 0 + 8
z = 0 + 8

Combine like terms: 0 + 8 = 8
z = 8

Simplifying
z = 8
Subproblem 2
Set the factor '(6 + -5z)' equal to zero and attempt to solve:

Simplifying
6 + -5z = 0

Solving
6 + -5z = 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 + -5z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5z = 0 + -6
-5z = 0 + -6

Combine like terms: 0 + -6 = -6
-5z = -6

Divide each side by '-5'.
z = 1.2

Simplifying
z = 1.2
Solution
z = {8, 1.2}