2(x+1)-3x(2x-5)=6x-3

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

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

Reorder the terms:
2(1 + x) + -3x(2x + -5) = 6x + -3
(1 * 2 + x * 2) + -3x(2x + -5) = 6x + -3
(2 + 2x) + -3x(2x + -5) = 6x + -3

Reorder the terms:
2 + 2x + -3x(-5 + 2x) = 6x + -3
2 + 2x + (-5 * -3x + 2x * -3x) = 6x + -3
2 + 2x + (15x + -6x2) = 6x + -3

Combine like terms: 2x + 15x = 17x
2 + 17x + -6x2 = 6x + -3

Reorder the terms:
2 + 17x + -6x2 = -3 + 6x

Solving
2 + 17x + -6x2 = -3 + 6x

Solving for variable 'x'.

Reorder the terms:
2 + 3 + 17x + -6x + -6x2 = -3 + 6x + 3 + -6x

Combine like terms: 2 + 3 = 5
5 + 17x + -6x + -6x2 = -3 + 6x + 3 + -6x

Combine like terms: 17x + -6x = 11x
5 + 11x + -6x2 = -3 + 6x + 3 + -6x

Reorder the terms:
5 + 11x + -6x2 = -3 + 3 + 6x + -6x

Combine like terms: -3 + 3 = 0
5 + 11x + -6x2 = 0 + 6x + -6x
5 + 11x + -6x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
5 + 11x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.8333333333 + -1.833333333x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -1.833333333x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -1.833333333x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -1.833333333x + x2 = 0 + 0.8333333333
-1.833333333x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-1.833333333x + x2 = 0.8333333333

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 = 0.8333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333x + x2 = 0.8333333333 + 0.8402777775

Combine like terms: 0.8333333333 + 0.8402777775 = 1.6736111108
0.8402777775 + -1.833333333x + x2 = 1.6736111108

Factor a perfect square on the left side:
(x + -0.9166666665)(x + -0.9166666665) = 1.6736111108

Calculate the square root of the right side: 1.293681225

Break this problem into two subproblems by setting 
(x + -0.9166666665) equal to 1.293681225 and -1.293681225.

Subproblem 1
x + -0.9166666665 = 1.293681225

Simplifying
x + -0.9166666665 = 1.293681225

Reorder the terms:
-0.9166666665 + x = 1.293681225

Solving
-0.9166666665 + x = 1.293681225

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 = 1.293681225 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + x = 1.293681225 + 0.9166666665
x = 1.293681225 + 0.9166666665

Combine like terms: 1.293681225 + 0.9166666665 = 2.2103478915
x = 2.2103478915

Simplifying
x = 2.2103478915

Subproblem 2
x + -0.9166666665 = -1.293681225

Simplifying
x + -0.9166666665 = -1.293681225

Reorder the terms:
-0.9166666665 + x = -1.293681225

Solving
-0.9166666665 + x = -1.293681225

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 = -1.293681225 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + x = -1.293681225 + 0.9166666665
x = -1.293681225 + 0.9166666665

Combine like terms: -1.293681225 + 0.9166666665 = -0.3770145585
x = -0.3770145585

Simplifying
x = -0.3770145585

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2103478915, -0.3770145585}