x^2+19x=-34

Solution for x^2+19x=-34 equation:

Simplifying
x2 + 19x = -34

Reorder the terms:
19x + x2 = -34

Solving
19x + x2 = -34

Solving for variable 'x'.

Reorder the terms:
34 + 19x + x2 = -34 + 34

Combine like terms: -34 + 34 = 0
34 + 19x + x2 = 0

Factor a trinomial.
(17 + x)(2 + x) = 0

Subproblem 1
Set the factor '(17 + x)' equal to zero and attempt to solve:

Simplifying
17 + x = 0

Solving
17 + x = 0

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

Add '-17' to each side of the equation.
17 + -17 + x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + x = 0 + -17
x = 0 + -17

Combine like terms: 0 + -17 = -17
x = -17

Simplifying
x = -17
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-17, -2}