(z-5)(z-1)=

Solution for (z-5)(z-1)= equation:

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

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

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

Multiply (-5 + z) * (-1 + z)
(-5(-1 + z) + z(-1 + z)) = 0
((-1 * -5 + z * -5) + z(-1 + z)) = 0
((5 + -5z) + z(-1 + z)) = 0
(5 + -5z + (-1 * z + z * z)) = 0
(5 + -5z + (-1z + z2)) = 0

Combine like terms: -5z + -1z = -6z
(5 + -6z + z2) = 0

Solving
5 + -6z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1z = 0 + -1

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

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

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

Simplifying
z = 1
Subproblem 2
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
Solution
z = {1, 5}