10-9z=z^2

Solution for 10-9z=z^2 equation:

Simplifying
10 + -9z = z2

Solving
10 + -9z = z2

Solving for variable 'z'.

Combine like terms: z2 + -1z2 = 0
10 + -9z + -1z2 = 0

Factor a trinomial.
(1 + -1z)(10 + z) = 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 '(10 + z)' equal to zero and attempt to solve:

Simplifying
10 + z = 0

Solving
10 + z = 0

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

Add '-10' to each side of the equation.
10 + -10 + z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + z = 0 + -10
z = 0 + -10

Combine like terms: 0 + -10 = -10
z = -10

Simplifying
z = -10
Solution
z = {1, -10}