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

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

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

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

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

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

Combine like terms: -8z + -6z = -14z
(48 + -14z + z2) = 0

Solving
48 + -14z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + -1z)(8 + -1z) = 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 '(8 + -1z)' equal to zero and attempt to solve:

Simplifying
8 + -1z = 0

Solving
8 + -1z = 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 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1z = 0 + -8
-1z = 0 + -8

Combine like terms: 0 + -8 = -8
-1z = -8

Divide each side by '-1'.
z = 8

Simplifying
z = 8
Solution
z = {6, 8}