k^2+19k=-90

Solution for k^2+19k=-90 equation:

Simplifying
k2 + 19k = -90

Reorder the terms:
19k + k2 = -90

Solving
19k + k2 = -90

Solving for variable 'k'.

Reorder the terms:
90 + 19k + k2 = -90 + 90

Combine like terms: -90 + 90 = 0
90 + 19k + k2 = 0

Factor a trinomial.
(10 + k)(9 + k) = 0

Subproblem 1
Set the factor '(10 + k)' equal to zero and attempt to solve:

Simplifying
10 + k = 0

Solving
10 + k = 0

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

Add '-10' to each side of the equation.
10 + -10 + k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + k = 0 + -10
k = 0 + -10

Combine like terms: 0 + -10 = -10
k = -10

Simplifying
k = -10
Subproblem 2
Set the factor '(9 + k)' equal to zero and attempt to solve:

Simplifying
9 + k = 0

Solving
9 + k = 0

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

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

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

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

Simplifying
k = -9
Solution
k = {-10, -9}