-3x(x+1)=2(x-8)+3

Solution for -3x(x+1)=2(x-8)+3 equation:

Simplifying
-3x(x + 1) = 2(x + -8) + 3

Reorder the terms:
-3x(1 + x) = 2(x + -8) + 3
(1 * -3x + x * -3x) = 2(x + -8) + 3
(-3x + -3x2) = 2(x + -8) + 3

Reorder the terms:
-3x + -3x2 = 2(-8 + x) + 3
-3x + -3x2 = (-8 * 2 + x * 2) + 3
-3x + -3x2 = (-16 + 2x) + 3

Reorder the terms:
-3x + -3x2 = -16 + 3 + 2x

Combine like terms: -16 + 3 = -13
-3x + -3x2 = -13 + 2x

Solving
-3x + -3x2 = -13 + 2x

Solving for variable 'x'.

Reorder the terms:
13 + -3x + -2x + -3x2 = -13 + 2x + 13 + -2x

Combine like terms: -3x + -2x = -5x
13 + -5x + -3x2 = -13 + 2x + 13 + -2x

Reorder the terms:
13 + -5x + -3x2 = -13 + 13 + 2x + -2x

Combine like terms: -13 + 13 = 0
13 + -5x + -3x2 = 0 + 2x + -2x
13 + -5x + -3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
13 + -5x + -3x2 = 0

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

Divide each side by '-3'.
-4.333333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + 1.666666667x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + 1.666666667x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 4.333333333
1.666666667x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
1.666666667x + x2 = 4.333333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 4.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 4.333333333 + 0.6944444447

Combine like terms: 4.333333333 + 0.6944444447 = 5.0277777777
0.6944444447 + 1.666666667x + x2 = 5.0277777777

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 5.0277777777

Calculate the square root of the right side: 2.242270674

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 2.242270674 and -2.242270674.

Subproblem 1
x + 0.8333333335 = 2.242270674

Simplifying
x + 0.8333333335 = 2.242270674

Reorder the terms:
0.8333333335 + x = 2.242270674

Solving
0.8333333335 + x = 2.242270674

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 2.242270674 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 2.242270674 + -0.8333333335
x = 2.242270674 + -0.8333333335

Combine like terms: 2.242270674 + -0.8333333335 = 1.4089373405
x = 1.4089373405

Simplifying
x = 1.4089373405

Subproblem 2
x + 0.8333333335 = -2.242270674

Simplifying
x + 0.8333333335 = -2.242270674

Reorder the terms:
0.8333333335 + x = -2.242270674

Solving
0.8333333335 + x = -2.242270674

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -2.242270674 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -2.242270674 + -0.8333333335
x = -2.242270674 + -0.8333333335

Combine like terms: -2.242270674 + -0.8333333335 = -3.0756040075
x = -3.0756040075

Simplifying
x = -3.0756040075

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4089373405, -3.0756040075}