z^2-z=-5+5z

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

Simplifying
z2 + -1z = -5 + 5z

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

Solving
-1z + z2 = -5 + 5z

Solving for variable 'z'.

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

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

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

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

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

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}