(6x+22)(x+37)=154

Solution for (6x+22)(x+37)=154 equation:

Simplifying
(6x + 22)(x + 37) = 154

Reorder the terms:
(22 + 6x)(x + 37) = 154

Reorder the terms:
(22 + 6x)(37 + x) = 154

Multiply (22 + 6x) * (37 + x)
(22(37 + x) + 6x * (37 + x)) = 154
((37 * 22 + x * 22) + 6x * (37 + x)) = 154
((814 + 22x) + 6x * (37 + x)) = 154
(814 + 22x + (37 * 6x + x * 6x)) = 154
(814 + 22x + (222x + 6x2)) = 154

Combine like terms: 22x + 222x = 244x
(814 + 244x + 6x2) = 154

Solving
814 + 244x + 6x2 = 154

Solving for variable 'x'.

Reorder the terms:
814 + -154 + 244x + 6x2 = 154 + -154

Combine like terms: 814 + -154 = 660
660 + 244x + 6x2 = 154 + -154

Combine like terms: 154 + -154 = 0
660 + 244x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(330 + 122x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(330 + 122x + 3x2)' equal to zero and attempt to solve:

Simplifying
330 + 122x + 3x2 = 0

Solving
330 + 122x + 3x2 = 0

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

Divide each side by '3'.
110 + 40.66666667x + x2 = 0

Move the constant term to the right:

Add '-110' to each side of the equation.
110 + 40.66666667x + -110 + x2 = 0 + -110

Reorder the terms:
110 + -110 + 40.66666667x + x2 = 0 + -110

Combine like terms: 110 + -110 = 0
0 + 40.66666667x + x2 = 0 + -110
40.66666667x + x2 = 0 + -110

Combine like terms: 0 + -110 = -110
40.66666667x + x2 = -110

The x term is 40.66666667x.  Take half its coefficient (20.33333334).
Square it (413.4444447) and add it to both sides.

Add '413.4444447' to each side of the equation.
40.66666667x + 413.4444447 + x2 = -110 + 413.4444447

Reorder the terms:
413.4444447 + 40.66666667x + x2 = -110 + 413.4444447

Combine like terms: -110 + 413.4444447 = 303.4444447
413.4444447 + 40.66666667x + x2 = 303.4444447

Factor a perfect square on the left side:
(x + 20.33333334)(x + 20.33333334) = 303.4444447

Calculate the square root of the right side: 17.419656848

Break this problem into two subproblems by setting 
(x + 20.33333334) equal to 17.419656848 and -17.419656848.

Subproblem 1
x + 20.33333334 = 17.419656848

Simplifying
x + 20.33333334 = 17.419656848

Reorder the terms:
20.33333334 + x = 17.419656848

Solving
20.33333334 + x = 17.419656848

Solving for variable 'x'.

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

Add '-20.33333334' to each side of the equation.
20.33333334 + -20.33333334 + x = 17.419656848 + -20.33333334

Combine like terms: 20.33333334 + -20.33333334 = 0.00000000
0.00000000 + x = 17.419656848 + -20.33333334
x = 17.419656848 + -20.33333334

Combine like terms: 17.419656848 + -20.33333334 = -2.913676492
x = -2.913676492

Simplifying
x = -2.913676492

Subproblem 2
x + 20.33333334 = -17.419656848

Simplifying
x + 20.33333334 = -17.419656848

Reorder the terms:
20.33333334 + x = -17.419656848

Solving
20.33333334 + x = -17.419656848

Solving for variable 'x'.

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

Add '-20.33333334' to each side of the equation.
20.33333334 + -20.33333334 + x = -17.419656848 + -20.33333334

Combine like terms: 20.33333334 + -20.33333334 = 0.00000000
0.00000000 + x = -17.419656848 + -20.33333334
x = -17.419656848 + -20.33333334

Combine like terms: -17.419656848 + -20.33333334 = -37.752990188
x = -37.752990188

Simplifying
x = -37.752990188

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.913676492, -37.752990188}
Solution
x = {-2.913676492, -37.752990188}