37x(2-8)(9x+7)=38

Solution for 37x(2-8)(9x+7)=38 equation:

Simplifying
37x(2 + -8)(9x + 7) = 38

Combine like terms: 2 + -8 = -6
37x(-6)(9x + 7) = 38

Reorder the terms:
37x * -6(7 + 9x) = 38

Reorder the terms for easier multiplication:
37 * -6x(7 + 9x) = 38

Multiply 37 * -6
-222x(7 + 9x) = 38
(7 * -222x + 9x * -222x) = 38
(-1554x + -1998x2) = 38

Solving
-1554x + -1998x2 = 38

Solving for variable 'x'.

Reorder the terms:
-38 + -1554x + -1998x2 = 38 + -38

Combine like terms: 38 + -38 = 0
-38 + -1554x + -1998x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(19 + 777x + 999x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(19 + 777x + 999x2)' equal to zero and attempt to solve:

Simplifying
19 + 777x + 999x2 = 0

Solving
19 + 777x + 999x2 = 0

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

Divide each side by '999'.
0.01901901902 + 0.7777777778x + x2 = 0

Move the constant term to the right:

Add '-0.01901901902' to each side of the equation.
0.01901901902 + 0.7777777778x + -0.01901901902 + x2 = 0 + -0.01901901902

Reorder the terms:
0.01901901902 + -0.01901901902 + 0.7777777778x + x2 = 0 + -0.01901901902

Combine like terms: 0.01901901902 + -0.01901901902 = 0.00000000000
0.00000000000 + 0.7777777778x + x2 = 0 + -0.01901901902
0.7777777778x + x2 = 0 + -0.01901901902

Combine like terms: 0 + -0.01901901902 = -0.01901901902
0.7777777778x + x2 = -0.01901901902

The x term is 0.7777777778x.  Take half its coefficient (0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
0.7777777778x + 0.1512345679 + x2 = -0.01901901902 + 0.1512345679

Reorder the terms:
0.1512345679 + 0.7777777778x + x2 = -0.01901901902 + 0.1512345679

Combine like terms: -0.01901901902 + 0.1512345679 = 0.13221554888
0.1512345679 + 0.7777777778x + x2 = 0.13221554888

Factor a perfect square on the left side:
(x + 0.3888888889)(x + 0.3888888889) = 0.13221554888

Calculate the square root of the right side: 0.363614561

Break this problem into two subproblems by setting 
(x + 0.3888888889) equal to 0.363614561 and -0.363614561.

Subproblem 1
x + 0.3888888889 = 0.363614561

Simplifying
x + 0.3888888889 = 0.363614561

Reorder the terms:
0.3888888889 + x = 0.363614561

Solving
0.3888888889 + x = 0.363614561

Solving for variable 'x'.

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

Add '-0.3888888889' to each side of the equation.
0.3888888889 + -0.3888888889 + x = 0.363614561 + -0.3888888889

Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000
0.0000000000 + x = 0.363614561 + -0.3888888889
x = 0.363614561 + -0.3888888889

Combine like terms: 0.363614561 + -0.3888888889 = -0.0252743279
x = -0.0252743279

Simplifying
x = -0.0252743279

Subproblem 2
x + 0.3888888889 = -0.363614561

Simplifying
x + 0.3888888889 = -0.363614561

Reorder the terms:
0.3888888889 + x = -0.363614561

Solving
0.3888888889 + x = -0.363614561

Solving for variable 'x'.

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

Add '-0.3888888889' to each side of the equation.
0.3888888889 + -0.3888888889 + x = -0.363614561 + -0.3888888889

Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000
0.0000000000 + x = -0.363614561 + -0.3888888889
x = -0.363614561 + -0.3888888889

Combine like terms: -0.363614561 + -0.3888888889 = -0.7525034499
x = -0.7525034499

Simplifying
x = -0.7525034499

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.0252743279, -0.7525034499}
Solution
x = {-0.0252743279, -0.7525034499}