x^2+19x+83=-7

Solution for x^2+19x+83=-7 equation:

Simplifying
x2 + 19x + 83 = -7

Reorder the terms:
83 + 19x + x2 = -7

Solving
83 + 19x + x2 = -7

Solving for variable 'x'.

Reorder the terms:
83 + 7 + 19x + x2 = -7 + 7

Combine like terms: 83 + 7 = 90
90 + 19x + x2 = -7 + 7

Combine like terms: -7 + 7 = 0
90 + 19x + x2 = 0

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

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

Simplifying
10 + x = 0

Solving
10 + x = 0

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

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

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

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

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

Simplifying
9 + x = 0

Solving
9 + x = 0

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

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

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

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

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