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

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

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

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

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

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

Combine like terms: -8z + -5z = -13z
(40 + -13z + z2) = 0

Solving
40 + -13z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + -1z)(8 + -1z) = 0

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

Simplifying
5 + -1z = 0

Solving
5 + -1z = 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 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
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 = {5, 8}