z(z+1)=9+z

Solution for z(z+1)=9+z equation:

Simplifying
z(z + 1) = 9 + z

Reorder the terms:
z(1 + z) = 9 + z
(1 * z + z * z) = 9 + z
(1z + z2) = 9 + z

Solving
1z + z2 = 9 + z

Solving for variable 'z'.

Reorder the terms:
-9 + 1z + -1z + z2 = 9 + z + -9 + -1z

Combine like terms: 1z + -1z = 0
-9 + 0 + z2 = 9 + z + -9 + -1z
-9 + z2 = 9 + z + -9 + -1z

Reorder the terms:
-9 + z2 = 9 + -9 + z + -1z

Combine like terms: 9 + -9 = 0
-9 + z2 = 0 + z + -1z
-9 + z2 = z + -1z

Combine like terms: z + -1z = 0
-9 + z2 = 0

Factor a difference between two squares.
(3 + z)(-3 + z) = 0

Subproblem 1
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(-3 + z)' equal to zero and attempt to solve:

Simplifying
-3 + z = 0

Solving
-3 + z = 0

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

Add '3' to each side of the equation.
-3 + 3 + z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + z = 0 + 3
z = 0 + 3

Combine like terms: 0 + 3 = 3
z = 3

Simplifying
z = 3
Solution
z = {-3, 3}