19(15x+1)-(-2x+10)(9x)=5

Solution for 19(15x+1)-(-2x+10)(9x)=5 equation:

Simplifying
19(15x + 1) + -1(-2x + 10)(9x) = 5

Reorder the terms:
19(1 + 15x) + -1(-2x + 10)(9x) = 5
(1 * 19 + 15x * 19) + -1(-2x + 10)(9x) = 5
(19 + 285x) + -1(-2x + 10)(9x) = 5

Reorder the terms:
19 + 285x + -1(10 + -2x)(9x) = 5

Remove parenthesis around (9x)
19 + 285x + -1(10 + -2x) * 9x = 5

Reorder the terms for easier multiplication:
19 + 285x + -1 * 9x(10 + -2x) = 5

Multiply -1 * 9
19 + 285x + -9x(10 + -2x) = 5
19 + 285x + (10 * -9x + -2x * -9x) = 5
19 + 285x + (-90x + 18x2) = 5

Combine like terms: 285x + -90x = 195x
19 + 195x + 18x2 = 5

Solving
19 + 195x + 18x2 = 5

Solving for variable 'x'.

Reorder the terms:
19 + -5 + 195x + 18x2 = 5 + -5

Combine like terms: 19 + -5 = 14
14 + 195x + 18x2 = 5 + -5

Combine like terms: 5 + -5 = 0
14 + 195x + 18x2 = 0

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

Divide each side by '18'.
0.7777777778 + 10.83333333x + x2 = 0

Move the constant term to the right:

Add '-0.7777777778' to each side of the equation.
0.7777777778 + 10.83333333x + -0.7777777778 + x2 = 0 + -0.7777777778

Reorder the terms:
0.7777777778 + -0.7777777778 + 10.83333333x + x2 = 0 + -0.7777777778

Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000
0.0000000000 + 10.83333333x + x2 = 0 + -0.7777777778
10.83333333x + x2 = 0 + -0.7777777778

Combine like terms: 0 + -0.7777777778 = -0.7777777778
10.83333333x + x2 = -0.7777777778

The x term is 10.83333333x.  Take half its coefficient (5.416666665).
Square it (29.34027776) and add it to both sides.

Add '29.34027776' to each side of the equation.
10.83333333x + 29.34027776 + x2 = -0.7777777778 + 29.34027776

Reorder the terms:
29.34027776 + 10.83333333x + x2 = -0.7777777778 + 29.34027776

Combine like terms: -0.7777777778 + 29.34027776 = 28.5624999822
29.34027776 + 10.83333333x + x2 = 28.5624999822

Factor a perfect square on the left side:
(x + 5.416666665)(x + 5.416666665) = 28.5624999822

Calculate the square root of the right side: 5.34438958

Break this problem into two subproblems by setting 
(x + 5.416666665) equal to 5.34438958 and -5.34438958.

Subproblem 1
x + 5.416666665 = 5.34438958

Simplifying
x + 5.416666665 = 5.34438958

Reorder the terms:
5.416666665 + x = 5.34438958

Solving
5.416666665 + x = 5.34438958

Solving for variable 'x'.

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

Add '-5.416666665' to each side of the equation.
5.416666665 + -5.416666665 + x = 5.34438958 + -5.416666665

Combine like terms: 5.416666665 + -5.416666665 = 0.000000000
0.000000000 + x = 5.34438958 + -5.416666665
x = 5.34438958 + -5.416666665

Combine like terms: 5.34438958 + -5.416666665 = -0.072277085
x = -0.072277085

Simplifying
x = -0.072277085

Subproblem 2
x + 5.416666665 = -5.34438958

Simplifying
x + 5.416666665 = -5.34438958

Reorder the terms:
5.416666665 + x = -5.34438958

Solving
5.416666665 + x = -5.34438958

Solving for variable 'x'.

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

Add '-5.416666665' to each side of the equation.
5.416666665 + -5.416666665 + x = -5.34438958 + -5.416666665

Combine like terms: 5.416666665 + -5.416666665 = 0.000000000
0.000000000 + x = -5.34438958 + -5.416666665
x = -5.34438958 + -5.416666665

Combine like terms: -5.34438958 + -5.416666665 = -10.761056245
x = -10.761056245

Simplifying
x = -10.761056245

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.072277085, -10.761056245}