7x(3x-10)=6+(x-9)

Solution for 7x(3x-10)=6+(x-9) equation:

Simplifying
7x(3x + -10) = 6 + (x + -9)

Reorder the terms:
7x(-10 + 3x) = 6 + (x + -9)
(-10 * 7x + 3x * 7x) = 6 + (x + -9)
(-70x + 21x2) = 6 + (x + -9)

Reorder the terms:
-70x + 21x2 = 6 + (-9 + x)

Remove parenthesis around (-9 + x)
-70x + 21x2 = 6 + -9 + x

Combine like terms: 6 + -9 = -3
-70x + 21x2 = -3 + x

Solving
-70x + 21x2 = -3 + x

Solving for variable 'x'.

Reorder the terms:
3 + -70x + -1x + 21x2 = -3 + x + 3 + -1x

Combine like terms: -70x + -1x = -71x
3 + -71x + 21x2 = -3 + x + 3 + -1x

Reorder the terms:
3 + -71x + 21x2 = -3 + 3 + x + -1x

Combine like terms: -3 + 3 = 0
3 + -71x + 21x2 = 0 + x + -1x
3 + -71x + 21x2 = x + -1x

Combine like terms: x + -1x = 0
3 + -71x + 21x2 = 0

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

Divide each side by '21'.
0.1428571429 + -3.380952381x + x2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -3.380952381x + -0.1428571429 + x2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + -3.380952381x + x2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + -3.380952381x + x2 = 0 + -0.1428571429
-3.380952381x + x2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
-3.380952381x + x2 = -0.1428571429

The x term is -3.380952381x.  Take half its coefficient (-1.690476191).
Square it (2.857709752) and add it to both sides.

Add '2.857709752' to each side of the equation.
-3.380952381x + 2.857709752 + x2 = -0.1428571429 + 2.857709752

Reorder the terms:
2.857709752 + -3.380952381x + x2 = -0.1428571429 + 2.857709752

Combine like terms: -0.1428571429 + 2.857709752 = 2.7148526091
2.857709752 + -3.380952381x + x2 = 2.7148526091

Factor a perfect square on the left side:
(x + -1.690476191)(x + -1.690476191) = 2.7148526091

Calculate the square root of the right side: 1.647680979

Break this problem into two subproblems by setting 
(x + -1.690476191) equal to 1.647680979 and -1.647680979.

Subproblem 1
x + -1.690476191 = 1.647680979

Simplifying
x + -1.690476191 = 1.647680979

Reorder the terms:
-1.690476191 + x = 1.647680979

Solving
-1.690476191 + x = 1.647680979

Solving for variable 'x'.

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

Add '1.690476191' to each side of the equation.
-1.690476191 + 1.690476191 + x = 1.647680979 + 1.690476191

Combine like terms: -1.690476191 + 1.690476191 = 0.000000000
0.000000000 + x = 1.647680979 + 1.690476191
x = 1.647680979 + 1.690476191

Combine like terms: 1.647680979 + 1.690476191 = 3.33815717
x = 3.33815717

Simplifying
x = 3.33815717

Subproblem 2
x + -1.690476191 = -1.647680979

Simplifying
x + -1.690476191 = -1.647680979

Reorder the terms:
-1.690476191 + x = -1.647680979

Solving
-1.690476191 + x = -1.647680979

Solving for variable 'x'.

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

Add '1.690476191' to each side of the equation.
-1.690476191 + 1.690476191 + x = -1.647680979 + 1.690476191

Combine like terms: -1.690476191 + 1.690476191 = 0.000000000
0.000000000 + x = -1.647680979 + 1.690476191
x = -1.647680979 + 1.690476191

Combine like terms: -1.647680979 + 1.690476191 = 0.042795212
x = 0.042795212

Simplifying
x = 0.042795212

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.33815717, 0.042795212}