9-6z+z^2=21-2z

Solution for 9-6z+z^2=21-2z equation:

Simplifying
9 + -6z + z2 = 21 + -2z

Solving
9 + -6z + z2 = 21 + -2z

Solving for variable 'z'.

Reorder the terms:
9 + -21 + -6z + 2z + z2 = 21 + -2z + -21 + 2z

Combine like terms: 9 + -21 = -12
-12 + -6z + 2z + z2 = 21 + -2z + -21 + 2z

Combine like terms: -6z + 2z = -4z
-12 + -4z + z2 = 21 + -2z + -21 + 2z

Reorder the terms:
-12 + -4z + z2 = 21 + -21 + -2z + 2z

Combine like terms: 21 + -21 = 0
-12 + -4z + z2 = 0 + -2z + 2z
-12 + -4z + z2 = -2z + 2z

Combine like terms: -2z + 2z = 0
-12 + -4z + z2 = 0

Factor a trinomial.
(-2 + -1z)(6 + -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 '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

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

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

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-2, 6}