112=(3x-1)(2x+1)

Solution for 112=(3x-1)(2x+1) equation:

Simplifying
112 = (3x + -1)(2x + 1)

Reorder the terms:
112 = (-1 + 3x)(2x + 1)

Reorder the terms:
112 = (-1 + 3x)(1 + 2x)

Multiply (-1 + 3x) * (1 + 2x)
112 = (-1(1 + 2x) + 3x * (1 + 2x))
112 = ((1 * -1 + 2x * -1) + 3x * (1 + 2x))
112 = ((-1 + -2x) + 3x * (1 + 2x))
112 = (-1 + -2x + (1 * 3x + 2x * 3x))
112 = (-1 + -2x + (3x + 6x2))

Combine like terms: -2x + 3x = 1x
112 = (-1 + 1x + 6x2)

Solving
112 = -1 + 1x + 6x2

Solving for variable 'x'.

Combine like terms: 112 + 1 = 113
113 + -1x + -6x2 = -1 + 1x + 6x2 + 1 + -1x + -6x2

Reorder the terms:
113 + -1x + -6x2 = -1 + 1 + 1x + -1x + 6x2 + -6x2

Combine like terms: -1 + 1 = 0
113 + -1x + -6x2 = 0 + 1x + -1x + 6x2 + -6x2
113 + -1x + -6x2 = 1x + -1x + 6x2 + -6x2

Combine like terms: 1x + -1x = 0
113 + -1x + -6x2 = 0 + 6x2 + -6x2
113 + -1x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
113 + -1x + -6x2 = 0

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

Divide each side by '-6'.
-18.83333333 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '18.83333333' to each side of the equation.
-18.83333333 + 0.1666666667x + 18.83333333 + x2 = 0 + 18.83333333

Reorder the terms:
-18.83333333 + 18.83333333 + 0.1666666667x + x2 = 0 + 18.83333333

Combine like terms: -18.83333333 + 18.83333333 = 0.00000000
0.00000000 + 0.1666666667x + x2 = 0 + 18.83333333
0.1666666667x + x2 = 0 + 18.83333333

Combine like terms: 0 + 18.83333333 = 18.83333333
0.1666666667x + x2 = 18.83333333

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 = 18.83333333 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 18.83333333 + 0.006944444447

Combine like terms: 18.83333333 + 0.006944444447 = 18.840277774447
0.006944444447 + 0.1666666667x + x2 = 18.840277774447

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 18.840277774447

Calculate the square root of the right side: 4.340538881

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 4.340538881 and -4.340538881.

Subproblem 1
x + 0.08333333335 = 4.340538881

Simplifying
x + 0.08333333335 = 4.340538881

Reorder the terms:
0.08333333335 + x = 4.340538881

Solving
0.08333333335 + x = 4.340538881

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 = 4.340538881 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = 4.340538881 + -0.08333333335
x = 4.340538881 + -0.08333333335

Combine like terms: 4.340538881 + -0.08333333335 = 4.25720554765
x = 4.25720554765

Simplifying
x = 4.25720554765

Subproblem 2
x + 0.08333333335 = -4.340538881

Simplifying
x + 0.08333333335 = -4.340538881

Reorder the terms:
0.08333333335 + x = -4.340538881

Solving
0.08333333335 + x = -4.340538881

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 = -4.340538881 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = -4.340538881 + -0.08333333335
x = -4.340538881 + -0.08333333335

Combine like terms: -4.340538881 + -0.08333333335 = -4.42387221435
x = -4.42387221435

Simplifying
x = -4.42387221435

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.25720554765, -4.42387221435}