4x(3-6x)7+6=19(8x-1)2+9

Solution for 4x(3-6x)7+6=19(8x-1)2+9 equation:

Simplifying
4x(3 + -6x) * 7 + 6 = 19(8x + -1) * 2 + 9

Reorder the terms for easier multiplication:
4 * 7x(3 + -6x) + 6 = 19(8x + -1) * 2 + 9

Multiply 4 * 7
28x(3 + -6x) + 6 = 19(8x + -1) * 2 + 9
(3 * 28x + -6x * 28x) + 6 = 19(8x + -1) * 2 + 9
(84x + -168x2) + 6 = 19(8x + -1) * 2 + 9

Reorder the terms:
6 + 84x + -168x2 = 19(8x + -1) * 2 + 9

Reorder the terms:
6 + 84x + -168x2 = 19(-1 + 8x) * 2 + 9

Reorder the terms for easier multiplication:
6 + 84x + -168x2 = 19 * 2(-1 + 8x) + 9

Multiply 19 * 2
6 + 84x + -168x2 = 38(-1 + 8x) + 9
6 + 84x + -168x2 = (-1 * 38 + 8x * 38) + 9
6 + 84x + -168x2 = (-38 + 304x) + 9

Reorder the terms:
6 + 84x + -168x2 = -38 + 9 + 304x

Combine like terms: -38 + 9 = -29
6 + 84x + -168x2 = -29 + 304x

Solving
6 + 84x + -168x2 = -29 + 304x

Solving for variable 'x'.

Reorder the terms:
6 + 29 + 84x + -304x + -168x2 = -29 + 304x + 29 + -304x

Combine like terms: 6 + 29 = 35
35 + 84x + -304x + -168x2 = -29 + 304x + 29 + -304x

Combine like terms: 84x + -304x = -220x
35 + -220x + -168x2 = -29 + 304x + 29 + -304x

Reorder the terms:
35 + -220x + -168x2 = -29 + 29 + 304x + -304x

Combine like terms: -29 + 29 = 0
35 + -220x + -168x2 = 0 + 304x + -304x
35 + -220x + -168x2 = 304x + -304x

Combine like terms: 304x + -304x = 0
35 + -220x + -168x2 = 0

Begin completing the square.  Divide all terms by
-168 the coefficient of the squared term: 

Divide each side by '-168'.
-0.2083333333 + 1.30952381x + x2 = 0

Move the constant term to the right:

Add '0.2083333333' to each side of the equation.
-0.2083333333 + 1.30952381x + 0.2083333333 + x2 = 0 + 0.2083333333

Reorder the terms:
-0.2083333333 + 0.2083333333 + 1.30952381x + x2 = 0 + 0.2083333333

Combine like terms: -0.2083333333 + 0.2083333333 = 0.0000000000
0.0000000000 + 1.30952381x + x2 = 0 + 0.2083333333
1.30952381x + x2 = 0 + 0.2083333333

Combine like terms: 0 + 0.2083333333 = 0.2083333333
1.30952381x + x2 = 0.2083333333

The x term is 1.30952381x.  Take half its coefficient (0.654761905).
Square it (0.4287131522) and add it to both sides.

Add '0.4287131522' to each side of the equation.
1.30952381x + 0.4287131522 + x2 = 0.2083333333 + 0.4287131522

Reorder the terms:
0.4287131522 + 1.30952381x + x2 = 0.2083333333 + 0.4287131522

Combine like terms: 0.2083333333 + 0.4287131522 = 0.6370464855
0.4287131522 + 1.30952381x + x2 = 0.6370464855

Factor a perfect square on the left side:
(x + 0.654761905)(x + 0.654761905) = 0.6370464855

Calculate the square root of the right side: 0.798151919

Break this problem into two subproblems by setting 
(x + 0.654761905) equal to 0.798151919 and -0.798151919.

Subproblem 1
x + 0.654761905 = 0.798151919

Simplifying
x + 0.654761905 = 0.798151919

Reorder the terms:
0.654761905 + x = 0.798151919

Solving
0.654761905 + x = 0.798151919

Solving for variable 'x'.

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

Add '-0.654761905' to each side of the equation.
0.654761905 + -0.654761905 + x = 0.798151919 + -0.654761905

Combine like terms: 0.654761905 + -0.654761905 = 0.000000000
0.000000000 + x = 0.798151919 + -0.654761905
x = 0.798151919 + -0.654761905

Combine like terms: 0.798151919 + -0.654761905 = 0.143390014
x = 0.143390014

Simplifying
x = 0.143390014

Subproblem 2
x + 0.654761905 = -0.798151919

Simplifying
x + 0.654761905 = -0.798151919

Reorder the terms:
0.654761905 + x = -0.798151919

Solving
0.654761905 + x = -0.798151919

Solving for variable 'x'.

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

Add '-0.654761905' to each side of the equation.
0.654761905 + -0.654761905 + x = -0.798151919 + -0.654761905

Combine like terms: 0.654761905 + -0.654761905 = 0.000000000
0.000000000 + x = -0.798151919 + -0.654761905
x = -0.798151919 + -0.654761905

Combine like terms: -0.798151919 + -0.654761905 = -1.452913824
x = -1.452913824

Simplifying
x = -1.452913824

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.143390014, -1.452913824}