6x^2+23x+18=0

Solution for 6x^2+23x+18=0 equation:

Simplifying
6x2 + 23x + 18 = 0

Reorder the terms:
18 + 23x + 6x2 = 0

Solving
18 + 23x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
3 + 3.833333333x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 3.833333333x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 3.833333333x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 3.833333333x + x2 = 0 + -3
3.833333333x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
3.833333333x + x2 = -3

The x term is 3.833333333x.  Take half its coefficient (1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
3.833333333x + 3.673611112 + x2 = -3 + 3.673611112

Reorder the terms:
3.673611112 + 3.833333333x + x2 = -3 + 3.673611112

Combine like terms: -3 + 3.673611112 = 0.673611112
3.673611112 + 3.833333333x + x2 = 0.673611112

Factor a perfect square on the left side:
(x + 1.916666667)(x + 1.916666667) = 0.673611112

Calculate the square root of the right side: 0.820738151

Break this problem into two subproblems by setting 
(x + 1.916666667) equal to 0.820738151 and -0.820738151.

Subproblem 1
x + 1.916666667 = 0.820738151

Simplifying
x + 1.916666667 = 0.820738151

Reorder the terms:
1.916666667 + x = 0.820738151

Solving
1.916666667 + x = 0.820738151

Solving for variable 'x'.

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

Add '-1.916666667' to each side of the equation.
1.916666667 + -1.916666667 + x = 0.820738151 + -1.916666667

Combine like terms: 1.916666667 + -1.916666667 = 0.000000000
0.000000000 + x = 0.820738151 + -1.916666667
x = 0.820738151 + -1.916666667

Combine like terms: 0.820738151 + -1.916666667 = -1.095928516
x = -1.095928516

Simplifying
x = -1.095928516

Subproblem 2
x + 1.916666667 = -0.820738151

Simplifying
x + 1.916666667 = -0.820738151

Reorder the terms:
1.916666667 + x = -0.820738151

Solving
1.916666667 + x = -0.820738151

Solving for variable 'x'.

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

Add '-1.916666667' to each side of the equation.
1.916666667 + -1.916666667 + x = -0.820738151 + -1.916666667

Combine like terms: 1.916666667 + -1.916666667 = 0.000000000
0.000000000 + x = -0.820738151 + -1.916666667
x = -0.820738151 + -1.916666667

Combine like terms: -0.820738151 + -1.916666667 = -2.737404818
x = -2.737404818

Simplifying
x = -2.737404818

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.095928516, -2.737404818}