z^2+13z=-42

Solution for z^2+13z=-42 equation:

Simplifying
z2 + 13z = -42

Reorder the terms:
13z + z2 = -42

Solving
13z + z2 = -42

Solving for variable 'z'.

Reorder the terms:
42 + 13z + z2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + 13z + z2 = 0

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

Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve:

Simplifying
7 + z = 0

Solving
7 + z = 0

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

Add '-7' to each side of the equation.
7 + -7 + z = 0 + -7

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

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

Simplifying
z = -7
Subproblem 2
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
Solution
z = {-7, -6}