2z-z^2=z-12

Solution for 2z-z^2=z-12 equation:

Simplifying
2z + -1z2 = z + -12

Reorder the terms:
2z + -1z2 = -12 + z

Solving
2z + -1z2 = -12 + z

Solving for variable 'z'.

Reorder the terms:
12 + 2z + -1z + -1z2 = -12 + z + 12 + -1z

Combine like terms: 2z + -1z = 1z
12 + 1z + -1z2 = -12 + z + 12 + -1z

Reorder the terms:
12 + 1z + -1z2 = -12 + 12 + z + -1z

Combine like terms: -12 + 12 = 0
12 + 1z + -1z2 = 0 + z + -1z
12 + 1z + -1z2 = z + -1z

Combine like terms: z + -1z = 0
12 + 1z + -1z2 = 0

Factor a trinomial.
(4 + -1z)(3 + z) = 0

Subproblem 1
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
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 = {4, -3}