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

Solution for -7x(2x-1)=4(2x+1)+6(3x-1) equation:

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

Reorder the terms:
-7x(-1 + 2x) = 4(2x + 1) + 6(3x + -1)
(-1 * -7x + 2x * -7x) = 4(2x + 1) + 6(3x + -1)
(7x + -14x2) = 4(2x + 1) + 6(3x + -1)

Reorder the terms:
7x + -14x2 = 4(1 + 2x) + 6(3x + -1)
7x + -14x2 = (1 * 4 + 2x * 4) + 6(3x + -1)
7x + -14x2 = (4 + 8x) + 6(3x + -1)

Reorder the terms:
7x + -14x2 = 4 + 8x + 6(-1 + 3x)
7x + -14x2 = 4 + 8x + (-1 * 6 + 3x * 6)
7x + -14x2 = 4 + 8x + (-6 + 18x)

Reorder the terms:
7x + -14x2 = 4 + -6 + 8x + 18x

Combine like terms: 4 + -6 = -2
7x + -14x2 = -2 + 8x + 18x

Combine like terms: 8x + 18x = 26x
7x + -14x2 = -2 + 26x

Solving
7x + -14x2 = -2 + 26x

Solving for variable 'x'.

Reorder the terms:
2 + 7x + -26x + -14x2 = -2 + 26x + 2 + -26x

Combine like terms: 7x + -26x = -19x
2 + -19x + -14x2 = -2 + 26x + 2 + -26x

Reorder the terms:
2 + -19x + -14x2 = -2 + 2 + 26x + -26x

Combine like terms: -2 + 2 = 0
2 + -19x + -14x2 = 0 + 26x + -26x
2 + -19x + -14x2 = 26x + -26x

Combine like terms: 26x + -26x = 0
2 + -19x + -14x2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
-0.1428571429 + 1.357142857x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 1.357142857x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 1.357142857x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 1.357142857x + x2 = 0 + 0.1428571429
1.357142857x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
1.357142857x + x2 = 0.1428571429

The x term is 1.357142857x.  Take half its coefficient (0.6785714285).
Square it (0.4604591836) and add it to both sides.

Add '0.4604591836' to each side of the equation.
1.357142857x + 0.4604591836 + x2 = 0.1428571429 + 0.4604591836

Reorder the terms:
0.4604591836 + 1.357142857x + x2 = 0.1428571429 + 0.4604591836

Combine like terms: 0.1428571429 + 0.4604591836 = 0.6033163265
0.4604591836 + 1.357142857x + x2 = 0.6033163265

Factor a perfect square on the left side:
(x + 0.6785714285)(x + 0.6785714285) = 0.6033163265

Calculate the square root of the right side: 0.776734399

Break this problem into two subproblems by setting 
(x + 0.6785714285) equal to 0.776734399 and -0.776734399.

Subproblem 1
x + 0.6785714285 = 0.776734399

Simplifying
x + 0.6785714285 = 0.776734399

Reorder the terms:
0.6785714285 + x = 0.776734399

Solving
0.6785714285 + x = 0.776734399

Solving for variable 'x'.

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

Add '-0.6785714285' to each side of the equation.
0.6785714285 + -0.6785714285 + x = 0.776734399 + -0.6785714285

Combine like terms: 0.6785714285 + -0.6785714285 = 0.0000000000
0.0000000000 + x = 0.776734399 + -0.6785714285
x = 0.776734399 + -0.6785714285

Combine like terms: 0.776734399 + -0.6785714285 = 0.0981629705
x = 0.0981629705

Simplifying
x = 0.0981629705

Subproblem 2
x + 0.6785714285 = -0.776734399

Simplifying
x + 0.6785714285 = -0.776734399

Reorder the terms:
0.6785714285 + x = -0.776734399

Solving
0.6785714285 + x = -0.776734399

Solving for variable 'x'.

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

Add '-0.6785714285' to each side of the equation.
0.6785714285 + -0.6785714285 + x = -0.776734399 + -0.6785714285

Combine like terms: 0.6785714285 + -0.6785714285 = 0.0000000000
0.0000000000 + x = -0.776734399 + -0.6785714285
x = -0.776734399 + -0.6785714285

Combine like terms: -0.776734399 + -0.6785714285 = -1.4553058275
x = -1.4553058275

Simplifying
x = -1.4553058275

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0981629705, -1.4553058275}