z^2=8+2z

Solution for z^2=8+2z equation:

Simplifying
z2 = 8 + 2z

Solving
z2 = 8 + 2z

Solving for variable 'z'.

Reorder the terms:
-8 + -2z + z2 = 8 + 2z + -8 + -2z

Reorder the terms:
-8 + -2z + z2 = 8 + -8 + 2z + -2z

Combine like terms: 8 + -8 = 0
-8 + -2z + z2 = 0 + 2z + -2z
-8 + -2z + z2 = 2z + -2z

Combine like terms: 2z + -2z = 0
-8 + -2z + z2 = 0

Factor a trinomial.
(-2 + -1z)(4 + -1z) = 0

Subproblem 1
Set the factor '(-2 + -1z)' equal to zero and attempt to solve:

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1z = 0 + 2
-1z = 0 + 2

Combine like terms: 0 + 2 = 2
-1z = 2

Divide each side by '-1'.
z = -2

Simplifying
z = -2
Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {-2, 4}