x^2+19x+84=234

Solution for x^2+19x+84=234 equation:

Simplifying
x2 + 19x + 84 = 234

Reorder the terms:
84 + 19x + x2 = 234

Solving
84 + 19x + x2 = 234

Solving for variable 'x'.

Reorder the terms:
84 + -234 + 19x + x2 = 234 + -234

Combine like terms: 84 + -234 = -150
-150 + 19x + x2 = 234 + -234

Combine like terms: 234 + -234 = 0
-150 + 19x + x2 = 0

Factor a trinomial.
(-25 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-25 + -1x)' equal to zero and attempt to solve:

Simplifying
-25 + -1x = 0

Solving
-25 + -1x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1x = 0 + 25
-1x = 0 + 25

Combine like terms: 0 + 25 = 25
-1x = 25

Divide each side by '-1'.
x = -25

Simplifying
x = -25
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-25, 6}