3(2x+1)=11(8-x)2(7x-4)

Solution for 3(2x+1)=11(8-x)2(7x-4) equation:

Simplifying
3(2x + 1) = 11(8 + -1x) * 2(7x + -4)

Reorder the terms:
3(1 + 2x) = 11(8 + -1x) * 2(7x + -4)
(1 * 3 + 2x * 3) = 11(8 + -1x) * 2(7x + -4)
(3 + 6x) = 11(8 + -1x) * 2(7x + -4)

Reorder the terms:
3 + 6x = 11(8 + -1x) * 2(-4 + 7x)

Reorder the terms for easier multiplication:
3 + 6x = 11 * 2(8 + -1x)(-4 + 7x)

Multiply 11 * 2
3 + 6x = 22(8 + -1x)(-4 + 7x)

Multiply (8 + -1x) * (-4 + 7x)
3 + 6x = 22(8(-4 + 7x) + -1x * (-4 + 7x))
3 + 6x = 22((-4 * 8 + 7x * 8) + -1x * (-4 + 7x))
3 + 6x = 22((-32 + 56x) + -1x * (-4 + 7x))
3 + 6x = 22(-32 + 56x + (-4 * -1x + 7x * -1x))
3 + 6x = 22(-32 + 56x + (4x + -7x2))

Combine like terms: 56x + 4x = 60x
3 + 6x = 22(-32 + 60x + -7x2)
3 + 6x = (-32 * 22 + 60x * 22 + -7x2 * 22)
3 + 6x = (-704 + 1320x + -154x2)

Solving
3 + 6x = -704 + 1320x + -154x2

Solving for variable 'x'.

Reorder the terms:
3 + 704 + 6x + -1320x + 154x2 = -704 + 1320x + -154x2 + 704 + -1320x + 154x2

Combine like terms: 3 + 704 = 707
707 + 6x + -1320x + 154x2 = -704 + 1320x + -154x2 + 704 + -1320x + 154x2

Combine like terms: 6x + -1320x = -1314x
707 + -1314x + 154x2 = -704 + 1320x + -154x2 + 704 + -1320x + 154x2

Reorder the terms:
707 + -1314x + 154x2 = -704 + 704 + 1320x + -1320x + -154x2 + 154x2

Combine like terms: -704 + 704 = 0
707 + -1314x + 154x2 = 0 + 1320x + -1320x + -154x2 + 154x2
707 + -1314x + 154x2 = 1320x + -1320x + -154x2 + 154x2

Combine like terms: 1320x + -1320x = 0
707 + -1314x + 154x2 = 0 + -154x2 + 154x2
707 + -1314x + 154x2 = -154x2 + 154x2

Combine like terms: -154x2 + 154x2 = 0
707 + -1314x + 154x2 = 0

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

Divide each side by '154'.
4.590909091 + -8.532467532x + x2 = 0

Move the constant term to the right:

Add '-4.590909091' to each side of the equation.
4.590909091 + -8.532467532x + -4.590909091 + x2 = 0 + -4.590909091

Reorder the terms:
4.590909091 + -4.590909091 + -8.532467532x + x2 = 0 + -4.590909091

Combine like terms: 4.590909091 + -4.590909091 = 0.000000000
0.000000000 + -8.532467532x + x2 = 0 + -4.590909091
-8.532467532x + x2 = 0 + -4.590909091

Combine like terms: 0 + -4.590909091 = -4.590909091
-8.532467532x + x2 = -4.590909091

The x term is -8.532467532x.  Take half its coefficient (-4.266233766).
Square it (18.20075055) and add it to both sides.

Add '18.20075055' to each side of the equation.
-8.532467532x + 18.20075055 + x2 = -4.590909091 + 18.20075055

Reorder the terms:
18.20075055 + -8.532467532x + x2 = -4.590909091 + 18.20075055

Combine like terms: -4.590909091 + 18.20075055 = 13.609841459
18.20075055 + -8.532467532x + x2 = 13.609841459

Factor a perfect square on the left side:
(x + -4.266233766)(x + -4.266233766) = 13.609841459

Calculate the square root of the right side: 3.689151862

Break this problem into two subproblems by setting 
(x + -4.266233766) equal to 3.689151862 and -3.689151862.

Subproblem 1
x + -4.266233766 = 3.689151862

Simplifying
x + -4.266233766 = 3.689151862

Reorder the terms:
-4.266233766 + x = 3.689151862

Solving
-4.266233766 + x = 3.689151862

Solving for variable 'x'.

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

Add '4.266233766' to each side of the equation.
-4.266233766 + 4.266233766 + x = 3.689151862 + 4.266233766

Combine like terms: -4.266233766 + 4.266233766 = 0.000000000
0.000000000 + x = 3.689151862 + 4.266233766
x = 3.689151862 + 4.266233766

Combine like terms: 3.689151862 + 4.266233766 = 7.955385628
x = 7.955385628

Simplifying
x = 7.955385628

Subproblem 2
x + -4.266233766 = -3.689151862

Simplifying
x + -4.266233766 = -3.689151862

Reorder the terms:
-4.266233766 + x = -3.689151862

Solving
-4.266233766 + x = -3.689151862

Solving for variable 'x'.

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

Add '4.266233766' to each side of the equation.
-4.266233766 + 4.266233766 + x = -3.689151862 + 4.266233766

Combine like terms: -4.266233766 + 4.266233766 = 0.000000000
0.000000000 + x = -3.689151862 + 4.266233766
x = -3.689151862 + 4.266233766

Combine like terms: -3.689151862 + 4.266233766 = 0.577081904
x = 0.577081904

Simplifying
x = 0.577081904

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.955385628, 0.577081904}