x^2+31x+84=0

Solution for x^2+31x+84=0 equation:

Simplifying
x2 + 31x + 84 = 0

Reorder the terms:
84 + 31x + x2 = 0

Solving
84 + 31x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(28 + x)(3 + x) = 0

Subproblem 1
Set the factor '(28 + x)' equal to zero and attempt to solve:

Simplifying
28 + x = 0

Solving
28 + x = 0

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

Add '-28' to each side of the equation.
28 + -28 + x = 0 + -28

Combine like terms: 28 + -28 = 0
0 + x = 0 + -28
x = 0 + -28

Combine like terms: 0 + -28 = -28
x = -28

Simplifying
x = -28
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-28, -3}