-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 = 14
14 + 3 + -21x + -5x + -16x + -1x + -6x2 = 0

Combine like terms: 14 + 3 = 17
17 + -21x + -5x + -16x + -1x + -6x2 = 0

Combine like terms: -21x + -5x = -26x
17 + -26x + -16x + -1x + -6x2 = 0

Combine like terms: -26x + -16x = -42x
17 + -42x + -1x + -6x2 = 0

Combine like terms: -42x + -1x = -43x
17 + -43x + -6x2 = 0

Solving
17 + -43x + -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'.
-2.833333333 + 7.166666667x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + 7.166666667x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + 7.166666667x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + 7.166666667x + x2 = 0 + 2.833333333
7.166666667x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
7.166666667x + x2 = 2.833333333

The x term is 7.166666667x.  Take half its coefficient (3.583333334).
Square it (12.84027778) and add it to both sides.

Add '12.84027778' to each side of the equation.
7.166666667x + 12.84027778 + x2 = 2.833333333 + 12.84027778

Reorder the terms:
12.84027778 + 7.166666667x + x2 = 2.833333333 + 12.84027778

Combine like terms: 2.833333333 + 12.84027778 = 15.673611113
12.84027778 + 7.166666667x + x2 = 15.673611113

Factor a perfect square on the left side:
(x + 3.583333334)(x + 3.583333334) = 15.673611113

Calculate the square root of the right side: 3.958991174

Break this problem into two subproblems by setting 
(x + 3.583333334) equal to 3.958991174 and -3.958991174.

Subproblem 1
x + 3.583333334 = 3.958991174

Simplifying
x + 3.583333334 = 3.958991174

Reorder the terms:
3.583333334 + x = 3.958991174

Solving
3.583333334 + x = 3.958991174

Solving for variable 'x'.

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

Add '-3.583333334' to each side of the equation.
3.583333334 + -3.583333334 + x = 3.958991174 + -3.583333334

Combine like terms: 3.583333334 + -3.583333334 = 0.000000000
0.000000000 + x = 3.958991174 + -3.583333334
x = 3.958991174 + -3.583333334

Combine like terms: 3.958991174 + -3.583333334 = 0.37565784
x = 0.37565784

Simplifying
x = 0.37565784

Subproblem 2
x + 3.583333334 = -3.958991174

Simplifying
x + 3.583333334 = -3.958991174

Reorder the terms:
3.583333334 + x = -3.958991174

Solving
3.583333334 + x = -3.958991174

Solving for variable 'x'.

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

Add '-3.583333334' to each side of the equation.
3.583333334 + -3.583333334 + x = -3.958991174 + -3.583333334

Combine like terms: 3.583333334 + -3.583333334 = 0.000000000
0.000000000 + x = -3.958991174 + -3.583333334
x = -3.958991174 + -3.583333334

Combine like terms: -3.958991174 + -3.583333334 = -7.542324508
x = -7.542324508

Simplifying
x = -7.542324508

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.37565784, -7.542324508}