z^2+14z=-45

Solution for z^2+14z=-45 equation:

Simplifying
z2 + 14z = -45

Reorder the terms:
14z + z2 = -45

Solving
14z + z2 = -45

Solving for variable 'z'.

Reorder the terms:
45 + 14z + z2 = -45 + 45

Combine like terms: -45 + 45 = 0
45 + 14z + z2 = 0

Factor a trinomial.
(9 + z)(5 + z) = 0

Subproblem 1
Set the factor '(9 + z)' equal to zero and attempt to solve:

Simplifying
9 + z = 0

Solving
9 + z = 0

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

Add '-9' to each side of the equation.
9 + -9 + z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + z = 0 + -9
z = 0 + -9

Combine like terms: 0 + -9 = -9
z = -9

Simplifying
z = -9
Subproblem 2
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
Solution
z = {-9, -5}