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

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

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

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

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

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

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

Multiply (-1 + 2x) * (4 + 3x)
6(-1(4 + 3x) + 2x * (4 + 3x)) = 11x
6((4 * -1 + 3x * -1) + 2x * (4 + 3x)) = 11x
6((-4 + -3x) + 2x * (4 + 3x)) = 11x
6(-4 + -3x + (4 * 2x + 3x * 2x)) = 11x
6(-4 + -3x + (8x + 6x2)) = 11x

Combine like terms: -3x + 8x = 5x
6(-4 + 5x + 6x2) = 11x
(-4 * 6 + 5x * 6 + 6x2 * 6) = 11x
(-24 + 30x + 36x2) = 11x

Solving
-24 + 30x + 36x2 = 11x

Solving for variable 'x'.

Reorder the terms:
-24 + 30x + -11x + 36x2 = 11x + -11x

Combine like terms: 30x + -11x = 19x
-24 + 19x + 36x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-24 + 19x + 36x2 = 0

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

Divide each side by '36'.
-0.6666666667 + 0.5277777778x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 0.5277777778x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 0.5277777778x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 0.5277777778x + x2 = 0 + 0.6666666667
0.5277777778x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
0.5277777778x + x2 = 0.6666666667

The x term is 0.5277777778x.  Take half its coefficient (0.2638888889).
Square it (0.06963734568) and add it to both sides.

Add '0.06963734568' to each side of the equation.
0.5277777778x + 0.06963734568 + x2 = 0.6666666667 + 0.06963734568

Reorder the terms:
0.06963734568 + 0.5277777778x + x2 = 0.6666666667 + 0.06963734568

Combine like terms: 0.6666666667 + 0.06963734568 = 0.73630401238
0.06963734568 + 0.5277777778x + x2 = 0.73630401238

Factor a perfect square on the left side:
(x + 0.2638888889)(x + 0.2638888889) = 0.73630401238

Calculate the square root of the right side: 0.858081588

Break this problem into two subproblems by setting 
(x + 0.2638888889) equal to 0.858081588 and -0.858081588.

Subproblem 1
x + 0.2638888889 = 0.858081588

Simplifying
x + 0.2638888889 = 0.858081588

Reorder the terms:
0.2638888889 + x = 0.858081588

Solving
0.2638888889 + x = 0.858081588

Solving for variable 'x'.

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

Add '-0.2638888889' to each side of the equation.
0.2638888889 + -0.2638888889 + x = 0.858081588 + -0.2638888889

Combine like terms: 0.2638888889 + -0.2638888889 = 0.0000000000
0.0000000000 + x = 0.858081588 + -0.2638888889
x = 0.858081588 + -0.2638888889

Combine like terms: 0.858081588 + -0.2638888889 = 0.5941926991
x = 0.5941926991

Simplifying
x = 0.5941926991

Subproblem 2
x + 0.2638888889 = -0.858081588

Simplifying
x + 0.2638888889 = -0.858081588

Reorder the terms:
0.2638888889 + x = -0.858081588

Solving
0.2638888889 + x = -0.858081588

Solving for variable 'x'.

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

Add '-0.2638888889' to each side of the equation.
0.2638888889 + -0.2638888889 + x = -0.858081588 + -0.2638888889

Combine like terms: 0.2638888889 + -0.2638888889 = 0.0000000000
0.0000000000 + x = -0.858081588 + -0.2638888889
x = -0.858081588 + -0.2638888889

Combine like terms: -0.858081588 + -0.2638888889 = -1.1219704769
x = -1.1219704769

Simplifying
x = -1.1219704769

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5941926991, -1.1219704769}