2x(6x+4)-6+2x=3(4x+3)+1

Solution for 2x(6x+4)-6+2x=3(4x+3)+1 equation:

Simplifying
2x(6x + 4) + -6 + 2x = 3(4x + 3) + 1

Reorder the terms:
2x(4 + 6x) + -6 + 2x = 3(4x + 3) + 1
(4 * 2x + 6x * 2x) + -6 + 2x = 3(4x + 3) + 1
(8x + 12x2) + -6 + 2x = 3(4x + 3) + 1

Reorder the terms:
-6 + 8x + 2x + 12x2 = 3(4x + 3) + 1

Combine like terms: 8x + 2x = 10x
-6 + 10x + 12x2 = 3(4x + 3) + 1

Reorder the terms:
-6 + 10x + 12x2 = 3(3 + 4x) + 1
-6 + 10x + 12x2 = (3 * 3 + 4x * 3) + 1
-6 + 10x + 12x2 = (9 + 12x) + 1

Reorder the terms:
-6 + 10x + 12x2 = 9 + 1 + 12x

Combine like terms: 9 + 1 = 10
-6 + 10x + 12x2 = 10 + 12x

Solving
-6 + 10x + 12x2 = 10 + 12x

Solving for variable 'x'.

Reorder the terms:
-6 + -10 + 10x + -12x + 12x2 = 10 + 12x + -10 + -12x

Combine like terms: -6 + -10 = -16
-16 + 10x + -12x + 12x2 = 10 + 12x + -10 + -12x

Combine like terms: 10x + -12x = -2x
-16 + -2x + 12x2 = 10 + 12x + -10 + -12x

Reorder the terms:
-16 + -2x + 12x2 = 10 + -10 + 12x + -12x

Combine like terms: 10 + -10 = 0
-16 + -2x + 12x2 = 0 + 12x + -12x
-16 + -2x + 12x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-16 + -2x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -1x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x + 6x2)' equal to zero and attempt to solve:

Simplifying
-8 + -1x + 6x2 = 0

Solving
-8 + -1x + 6x2 = 0

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

Divide each side by '6'.
-1.333333333 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -0.1666666667x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -0.1666666667x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -0.1666666667x + x2 = 0 + 1.333333333
-0.1666666667x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-0.1666666667x + x2 = 1.333333333

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 1.333333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 1.333333333 + 0.006944444447

Combine like terms: 1.333333333 + 0.006944444447 = 1.340277777447
0.006944444447 + -0.1666666667x + x2 = 1.340277777447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 1.340277777447

Calculate the square root of the right side: 1.157703666

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 1.157703666 and -1.157703666.

Subproblem 1
x + -0.08333333335 = 1.157703666

Simplifying
x + -0.08333333335 = 1.157703666

Reorder the terms:
-0.08333333335 + x = 1.157703666

Solving
-0.08333333335 + x = 1.157703666

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = 1.157703666 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 1.157703666 + 0.08333333335
x = 1.157703666 + 0.08333333335

Combine like terms: 1.157703666 + 0.08333333335 = 1.24103699935
x = 1.24103699935

Simplifying
x = 1.24103699935

Subproblem 2
x + -0.08333333335 = -1.157703666

Simplifying
x + -0.08333333335 = -1.157703666

Reorder the terms:
-0.08333333335 + x = -1.157703666

Solving
-0.08333333335 + x = -1.157703666

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = -1.157703666 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -1.157703666 + 0.08333333335
x = -1.157703666 + 0.08333333335

Combine like terms: -1.157703666 + 0.08333333335 = -1.07437033265
x = -1.07437033265

Simplifying
x = -1.07437033265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.24103699935, -1.07437033265}
Solution
x = {1.24103699935, -1.07437033265}