z^2+12z=-11

Solution for z^2+12z=-11 equation:

Simplifying
z2 + 12z = -11

Reorder the terms:
12z + z2 = -11

Solving
12z + z2 = -11

Solving for variable 'z'.

Reorder the terms:
11 + 12z + z2 = -11 + 11

Combine like terms: -11 + 11 = 0
11 + 12z + z2 = 0

Factor a trinomial.
(11 + z)(1 + z) = 0

Subproblem 1
Set the factor '(11 + z)' equal to zero and attempt to solve:

Simplifying
11 + z = 0

Solving
11 + z = 0

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

Add '-11' to each side of the equation.
11 + -11 + z = 0 + -11

Combine like terms: 11 + -11 = 0
0 + z = 0 + -11
z = 0 + -11

Combine like terms: 0 + -11 = -11
z = -11

Simplifying
z = -11
Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 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 + z = 0 + -1

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

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

Simplifying
z = -1
Solution
z = {-11, -1}