4x-2=7x(x+3)+(-x-6)

Solution for 4x-2=7x(x+3)+(-x-6) equation:

Simplifying
4x + -2 = 7x(x + 3) + (-1x + -6)

Reorder the terms:
-2 + 4x = 7x(x + 3) + (-1x + -6)

Reorder the terms:
-2 + 4x = 7x(3 + x) + (-1x + -6)
-2 + 4x = (3 * 7x + x * 7x) + (-1x + -6)
-2 + 4x = (21x + 7x2) + (-1x + -6)

Reorder the terms:
-2 + 4x = 21x + 7x2 + (-6 + -1x)

Remove parenthesis around (-6 + -1x)
-2 + 4x = 21x + 7x2 + -6 + -1x

Reorder the terms:
-2 + 4x = -6 + 21x + -1x + 7x2

Combine like terms: 21x + -1x = 20x
-2 + 4x = -6 + 20x + 7x2

Solving
-2 + 4x = -6 + 20x + 7x2

Solving for variable 'x'.

Reorder the terms:
-2 + 6 + 4x + -20x + -7x2 = -6 + 20x + 7x2 + 6 + -20x + -7x2

Combine like terms: -2 + 6 = 4
4 + 4x + -20x + -7x2 = -6 + 20x + 7x2 + 6 + -20x + -7x2

Combine like terms: 4x + -20x = -16x
4 + -16x + -7x2 = -6 + 20x + 7x2 + 6 + -20x + -7x2

Reorder the terms:
4 + -16x + -7x2 = -6 + 6 + 20x + -20x + 7x2 + -7x2

Combine like terms: -6 + 6 = 0
4 + -16x + -7x2 = 0 + 20x + -20x + 7x2 + -7x2
4 + -16x + -7x2 = 20x + -20x + 7x2 + -7x2

Combine like terms: 20x + -20x = 0
4 + -16x + -7x2 = 0 + 7x2 + -7x2
4 + -16x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
4 + -16x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.5714285714 + 2.285714286x + x2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 2.285714286x + 0.5714285714 + x2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 2.285714286x + x2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 2.285714286x + x2 = 0 + 0.5714285714
2.285714286x + x2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
2.285714286x + x2 = 0.5714285714

The x term is 2.285714286x.  Take half its coefficient (1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
2.285714286x + 1.306122449 + x2 = 0.5714285714 + 1.306122449

Reorder the terms:
1.306122449 + 2.285714286x + x2 = 0.5714285714 + 1.306122449

Combine like terms: 0.5714285714 + 1.306122449 = 1.8775510204
1.306122449 + 2.285714286x + x2 = 1.8775510204

Factor a perfect square on the left side:
(x + 1.142857143)(x + 1.142857143) = 1.8775510204

Calculate the square root of the right side: 1.370237578

Break this problem into two subproblems by setting 
(x + 1.142857143) equal to 1.370237578 and -1.370237578.

Subproblem 1
x + 1.142857143 = 1.370237578

Simplifying
x + 1.142857143 = 1.370237578

Reorder the terms:
1.142857143 + x = 1.370237578

Solving
1.142857143 + x = 1.370237578

Solving for variable 'x'.

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

Add '-1.142857143' to each side of the equation.
1.142857143 + -1.142857143 + x = 1.370237578 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + x = 1.370237578 + -1.142857143
x = 1.370237578 + -1.142857143

Combine like terms: 1.370237578 + -1.142857143 = 0.227380435
x = 0.227380435

Simplifying
x = 0.227380435

Subproblem 2
x + 1.142857143 = -1.370237578

Simplifying
x + 1.142857143 = -1.370237578

Reorder the terms:
1.142857143 + x = -1.370237578

Solving
1.142857143 + x = -1.370237578

Solving for variable 'x'.

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

Add '-1.142857143' to each side of the equation.
1.142857143 + -1.142857143 + x = -1.370237578 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + x = -1.370237578 + -1.142857143
x = -1.370237578 + -1.142857143

Combine like terms: -1.370237578 + -1.142857143 = -2.513094721
x = -2.513094721

Simplifying
x = -2.513094721

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.227380435, -2.513094721}