=6(x-6)+7x(3x+8)

Solution for =6(x-6)+7x(3x+8) equation:

Simplifying
0 = 6(x + -6) + 7x(3x + 8)

Reorder the terms:
0 = 6(-6 + x) + 7x(3x + 8)
0 = (-6 * 6 + x * 6) + 7x(3x + 8)
0 = (-36 + 6x) + 7x(3x + 8)

Reorder the terms:
0 = -36 + 6x + 7x(8 + 3x)
0 = -36 + 6x + (8 * 7x + 3x * 7x)
0 = -36 + 6x + (56x + 21x2)

Combine like terms: 6x + 56x = 62x
0 = -36 + 62x + 21x2

Solving
0 = -36 + 62x + 21x2

Solving for variable 'x'.

Combine like terms: 0 + 36 = 36
36 + -62x + -21x2 = -36 + 62x + 21x2 + 36 + -62x + -21x2

Reorder the terms:
36 + -62x + -21x2 = -36 + 36 + 62x + -62x + 21x2 + -21x2

Combine like terms: -36 + 36 = 0
36 + -62x + -21x2 = 0 + 62x + -62x + 21x2 + -21x2
36 + -62x + -21x2 = 62x + -62x + 21x2 + -21x2

Combine like terms: 62x + -62x = 0
36 + -62x + -21x2 = 0 + 21x2 + -21x2
36 + -62x + -21x2 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
36 + -62x + -21x2 = 0

Begin completing the square.  Divide all terms by
-21 the coefficient of the squared term: 

Divide each side by '-21'.
-1.714285714 + 2.952380952x + x2 = 0

Move the constant term to the right:

Add '1.714285714' to each side of the equation.
-1.714285714 + 2.952380952x + 1.714285714 + x2 = 0 + 1.714285714

Reorder the terms:
-1.714285714 + 1.714285714 + 2.952380952x + x2 = 0 + 1.714285714

Combine like terms: -1.714285714 + 1.714285714 = 0.000000000
0.000000000 + 2.952380952x + x2 = 0 + 1.714285714
2.952380952x + x2 = 0 + 1.714285714

Combine like terms: 0 + 1.714285714 = 1.714285714
2.952380952x + x2 = 1.714285714

The x term is 2.952380952x.  Take half its coefficient (1.476190476).
Square it (2.179138321) and add it to both sides.

Add '2.179138321' to each side of the equation.
2.952380952x + 2.179138321 + x2 = 1.714285714 + 2.179138321

Reorder the terms:
2.179138321 + 2.952380952x + x2 = 1.714285714 + 2.179138321

Combine like terms: 1.714285714 + 2.179138321 = 3.893424035
2.179138321 + 2.952380952x + x2 = 3.893424035

Factor a perfect square on the left side:
(x + 1.476190476)(x + 1.476190476) = 3.893424035

Calculate the square root of the right side: 1.973176129

Break this problem into two subproblems by setting 
(x + 1.476190476) equal to 1.973176129 and -1.973176129.

Subproblem 1
x + 1.476190476 = 1.973176129

Simplifying
x + 1.476190476 = 1.973176129

Reorder the terms:
1.476190476 + x = 1.973176129

Solving
1.476190476 + x = 1.973176129

Solving for variable 'x'.

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

Add '-1.476190476' to each side of the equation.
1.476190476 + -1.476190476 + x = 1.973176129 + -1.476190476

Combine like terms: 1.476190476 + -1.476190476 = 0.000000000
0.000000000 + x = 1.973176129 + -1.476190476
x = 1.973176129 + -1.476190476

Combine like terms: 1.973176129 + -1.476190476 = 0.496985653
x = 0.496985653

Simplifying
x = 0.496985653

Subproblem 2
x + 1.476190476 = -1.973176129

Simplifying
x + 1.476190476 = -1.973176129

Reorder the terms:
1.476190476 + x = -1.973176129

Solving
1.476190476 + x = -1.973176129

Solving for variable 'x'.

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

Add '-1.476190476' to each side of the equation.
1.476190476 + -1.476190476 + x = -1.973176129 + -1.476190476

Combine like terms: 1.476190476 + -1.476190476 = 0.000000000
0.000000000 + x = -1.973176129 + -1.476190476
x = -1.973176129 + -1.476190476

Combine like terms: -1.973176129 + -1.476190476 = -3.449366605
x = -3.449366605

Simplifying
x = -3.449366605

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.496985653, -3.449366605}