0=x^2+24x+119

Solution for 0=x^2+24x+119 equation:

Simplifying
0 = x2 + 24x + 119

Reorder the terms:
0 = 119 + 24x + x2

Solving
0 = 119 + 24x + x2

Solving for variable 'x'.

Combine like terms: 0 + -119 = -119
-119 + -24x + -1x2 = 119 + 24x + x2 + -119 + -24x + -1x2

Reorder the terms:
-119 + -24x + -1x2 = 119 + -119 + 24x + -24x + x2 + -1x2

Combine like terms: 119 + -119 = 0
-119 + -24x + -1x2 = 0 + 24x + -24x + x2 + -1x2
-119 + -24x + -1x2 = 24x + -24x + x2 + -1x2

Combine like terms: 24x + -24x = 0
-119 + -24x + -1x2 = 0 + x2 + -1x2
-119 + -24x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-119 + -24x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(119 + 24x + x2) = 0

Factor a trinomial.
-1((17 + x)(7 + x)) = 0

Ignore the factor -1.
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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {-17, -7}