6x^2+23x+22=0

Solution for 6x^2+23x+22=0 equation:

Simplifying
6x2 + 23x + 22 = 0

Reorder the terms:
22 + 23x + 6x2 = 0

Solving
22 + 23x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + x)(11 + 6x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(11 + 6x)' equal to zero and attempt to solve:

Simplifying
11 + 6x = 0

Solving
11 + 6x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 6x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 6x = 0 + -11
6x = 0 + -11

Combine like terms: 0 + -11 = -11
6x = -11

Divide each side by '6'.
x = -1.833333333

Simplifying
x = -1.833333333
Solution
x = {-2, -1.833333333}