z^2+14z+13=-35

Solution for z^2+14z+13=-35 equation:

Simplifying
z2 + 14z + 13 = -35

Reorder the terms:
13 + 14z + z2 = -35

Solving
13 + 14z + z2 = -35

Solving for variable 'z'.

Reorder the terms:
13 + 35 + 14z + z2 = -35 + 35

Combine like terms: 13 + 35 = 48
48 + 14z + z2 = -35 + 35

Combine like terms: -35 + 35 = 0
48 + 14z + z2 = 0

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

Subproblem 1
Set the factor '(8 + z)' equal to zero and attempt to solve:

Simplifying
8 + z = 0

Solving
8 + z = 0

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

Add '-8' to each side of the equation.
8 + -8 + z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + z = 0 + -8
z = 0 + -8

Combine like terms: 0 + -8 = -8
z = -8

Simplifying
z = -8
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 = {-8, -6}