z^2=-7z-6

Solution for z^2=-7z-6 equation:

Simplifying
z2 = -7z + -6

Reorder the terms:
z2 = -6 + -7z

Solving
z2 = -6 + -7z

Solving for variable 'z'.

Reorder the terms:
6 + 7z + z2 = -6 + -7z + 6 + 7z

Reorder the terms:
6 + 7z + z2 = -6 + 6 + -7z + 7z

Combine like terms: -6 + 6 = 0
6 + 7z + z2 = 0 + -7z + 7z
6 + 7z + z2 = -7z + 7z

Combine like terms: -7z + 7z = 0
6 + 7z + z2 = 0

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

Subproblem 1
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 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 + z = 0 + -6

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

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

Simplifying
z = -6
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 = {-6, -1}