-3x(2x+7)+(-5x+6)-8(1-2x)-(x-3)=0

Solution for -3x(2x+7)+(-5x+6)-8(1-2x)-(x-3)=0 equation:

Simplifying
-3x(2x + 7) + (-5x + 6) + -8(1 + -2x) + -1(x + -3) = 0

Reorder the terms:
-3x(7 + 2x) + (-5x + 6) + -8(1 + -2x) + -1(x + -3) = 0
(7 * -3x + 2x * -3x) + (-5x + 6) + -8(1 + -2x) + -1(x + -3) = 0
(-21x + -6x2) + (-5x + 6) + -8(1 + -2x) + -1(x + -3) = 0

Reorder the terms:
-21x + -6x2 + (6 + -5x) + -8(1 + -2x) + -1(x + -3) = 0

Remove parenthesis around (6 + -5x)
-21x + -6x2 + 6 + -5x + -8(1 + -2x) + -1(x + -3) = 0
-21x + -6x2 + 6 + -5x + (1 * -8 + -2x * -8) + -1(x + -3) = 0
-21x + -6x2 + 6 + -5x + (-8 + 16x) + -1(x + -3) = 0

Reorder the terms:
-21x + -6x2 + 6 + -5x + -8 + 16x + -1(-3 + x) = 0
-21x + -6x2 + 6 + -5x + -8 + 16x + (-3 * -1 + x * -1) = 0
-21x + -6x2 + 6 + -5x + -8 + 16x + (3 + -1x) = 0

Reorder the terms:
6 + -8 + 3 + -21x + -5x + 16x + -1x + -6x2 = 0

Combine like terms: 6 + -8 = -2
-2 + 3 + -21x + -5x + 16x + -1x + -6x2 = 0

Combine like terms: -2 + 3 = 1
1 + -21x + -5x + 16x + -1x + -6x2 = 0

Combine like terms: -21x + -5x = -26x
1 + -26x + 16x + -1x + -6x2 = 0

Combine like terms: -26x + 16x = -10x
1 + -10x + -1x + -6x2 = 0

Combine like terms: -10x + -1x = -11x
1 + -11x + -6x2 = 0

Solving
1 + -11x + -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'.
-0.1666666667 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 1.833333333x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 1.833333333x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 1.833333333x + x2 = 0 + 0.1666666667
1.833333333x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
1.833333333x + x2 = 0.1666666667

The x term is 1.833333333x.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333x + 0.8402777775 + x2 = 0.1666666667 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = 0.1666666667 + 0.8402777775

Combine like terms: 0.1666666667 + 0.8402777775 = 1.0069444442
0.8402777775 + 1.833333333x + x2 = 1.0069444442

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = 1.0069444442

Calculate the square root of the right side: 1.003466215

Break this problem into two subproblems by setting 
(x + 0.9166666665) equal to 1.003466215 and -1.003466215.

Subproblem 1
x + 0.9166666665 = 1.003466215

Simplifying
x + 0.9166666665 = 1.003466215

Reorder the terms:
0.9166666665 + x = 1.003466215

Solving
0.9166666665 + x = 1.003466215

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = 1.003466215 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = 1.003466215 + -0.9166666665
x = 1.003466215 + -0.9166666665

Combine like terms: 1.003466215 + -0.9166666665 = 0.0867995485
x = 0.0867995485

Simplifying
x = 0.0867995485

Subproblem 2
x + 0.9166666665 = -1.003466215

Simplifying
x + 0.9166666665 = -1.003466215

Reorder the terms:
0.9166666665 + x = -1.003466215

Solving
0.9166666665 + x = -1.003466215

Solving for variable 'x'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + x = -1.003466215 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + x = -1.003466215 + -0.9166666665
x = -1.003466215 + -0.9166666665

Combine like terms: -1.003466215 + -0.9166666665 = -1.9201328815
x = -1.9201328815

Simplifying
x = -1.9201328815

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0867995485, -1.9201328815}