(3x-1)*(2x+1)=14x+1

Solution for (3x-1)*(2x+1)=14x+1 equation:

Simplifying
(3x + -1)(2x + 1) = 14x + 1

Reorder the terms:
(-1 + 3x)(2x + 1) = 14x + 1

Reorder the terms:
(-1 + 3x)(1 + 2x) = 14x + 1

Multiply (-1 + 3x) * (1 + 2x)
(-1(1 + 2x) + 3x * (1 + 2x)) = 14x + 1
((1 * -1 + 2x * -1) + 3x * (1 + 2x)) = 14x + 1
((-1 + -2x) + 3x * (1 + 2x)) = 14x + 1
(-1 + -2x + (1 * 3x + 2x * 3x)) = 14x + 1
(-1 + -2x + (3x + 6x2)) = 14x + 1

Combine like terms: -2x + 3x = 1x
(-1 + 1x + 6x2) = 14x + 1

Reorder the terms:
-1 + 1x + 6x2 = 1 + 14x

Solving
-1 + 1x + 6x2 = 1 + 14x

Solving for variable 'x'.

Reorder the terms:
-1 + -1 + 1x + -14x + 6x2 = 1 + 14x + -1 + -14x

Combine like terms: -1 + -1 = -2
-2 + 1x + -14x + 6x2 = 1 + 14x + -1 + -14x

Combine like terms: 1x + -14x = -13x
-2 + -13x + 6x2 = 1 + 14x + -1 + -14x

Reorder the terms:
-2 + -13x + 6x2 = 1 + -1 + 14x + -14x

Combine like terms: 1 + -1 = 0
-2 + -13x + 6x2 = 0 + 14x + -14x
-2 + -13x + 6x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-2 + -13x + 6x2 = 0

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

Divide each side by '6'.
-0.3333333333 + -2.166666667x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -2.166666667x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -2.166666667x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -2.166666667x + x2 = 0 + 0.3333333333
-2.166666667x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-2.166666667x + x2 = 0.3333333333

The x term is -2.166666667x.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667x + 1.173611113 + x2 = 0.3333333333 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667x + x2 = 0.3333333333 + 1.173611113

Combine like terms: 0.3333333333 + 1.173611113 = 1.5069444463
1.173611113 + -2.166666667x + x2 = 1.5069444463

Factor a perfect square on the left side:
(x + -1.083333334)(x + -1.083333334) = 1.5069444463

Calculate the square root of the right side: 1.227576656

Break this problem into two subproblems by setting 
(x + -1.083333334) equal to 1.227576656 and -1.227576656.

Subproblem 1
x + -1.083333334 = 1.227576656

Simplifying
x + -1.083333334 = 1.227576656

Reorder the terms:
-1.083333334 + x = 1.227576656

Solving
-1.083333334 + x = 1.227576656

Solving for variable 'x'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + x = 1.227576656 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + x = 1.227576656 + 1.083333334
x = 1.227576656 + 1.083333334

Combine like terms: 1.227576656 + 1.083333334 = 2.31090999
x = 2.31090999

Simplifying
x = 2.31090999

Subproblem 2
x + -1.083333334 = -1.227576656

Simplifying
x + -1.083333334 = -1.227576656

Reorder the terms:
-1.083333334 + x = -1.227576656

Solving
-1.083333334 + x = -1.227576656

Solving for variable 'x'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + x = -1.227576656 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + x = -1.227576656 + 1.083333334
x = -1.227576656 + 1.083333334

Combine like terms: -1.227576656 + 1.083333334 = -0.144243322
x = -0.144243322

Simplifying
x = -0.144243322

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.31090999, -0.144243322}