0=z^2-6z+5

Solution for 0=z^2-6z+5 equation:

Simplifying
0 = z2 + -6z + 5

Reorder the terms:
0 = 5 + -6z + z2

Solving
0 = 5 + -6z + z2

Solving for variable 'z'.

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

Reorder the terms:
-5 + 6z + -1z2 = 5 + -5 + -6z + 6z + z2 + -1z2

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

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

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

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

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

Simplifying
-5 + z = 0

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

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

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

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