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

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

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

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

Remove parenthesis around (-2 + 4x)
-2 + 4x + (3x + 1) = (3x + 1)(4x + -2)

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

Remove parenthesis around (1 + 3x)
-2 + 4x + 1 + 3x = (3x + 1)(4x + -2)

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

Combine like terms: -2 + 1 = -1
-1 + 4x + 3x = (3x + 1)(4x + -2)

Combine like terms: 4x + 3x = 7x
-1 + 7x = (3x + 1)(4x + -2)

Reorder the terms:
-1 + 7x = (1 + 3x)(4x + -2)

Reorder the terms:
-1 + 7x = (1 + 3x)(-2 + 4x)

Multiply (1 + 3x) * (-2 + 4x)
-1 + 7x = (1(-2 + 4x) + 3x * (-2 + 4x))
-1 + 7x = ((-2 * 1 + 4x * 1) + 3x * (-2 + 4x))
-1 + 7x = ((-2 + 4x) + 3x * (-2 + 4x))
-1 + 7x = (-2 + 4x + (-2 * 3x + 4x * 3x))
-1 + 7x = (-2 + 4x + (-6x + 12x2))

Combine like terms: 4x + -6x = -2x
-1 + 7x = (-2 + -2x + 12x2)

Solving
-1 + 7x = -2 + -2x + 12x2

Solving for variable 'x'.

Reorder the terms:
-1 + 2 + 7x + 2x + -12x2 = -2 + -2x + 12x2 + 2 + 2x + -12x2

Combine like terms: -1 + 2 = 1
1 + 7x + 2x + -12x2 = -2 + -2x + 12x2 + 2 + 2x + -12x2

Combine like terms: 7x + 2x = 9x
1 + 9x + -12x2 = -2 + -2x + 12x2 + 2 + 2x + -12x2

Reorder the terms:
1 + 9x + -12x2 = -2 + 2 + -2x + 2x + 12x2 + -12x2

Combine like terms: -2 + 2 = 0
1 + 9x + -12x2 = 0 + -2x + 2x + 12x2 + -12x2
1 + 9x + -12x2 = -2x + 2x + 12x2 + -12x2

Combine like terms: -2x + 2x = 0
1 + 9x + -12x2 = 0 + 12x2 + -12x2
1 + 9x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
1 + 9x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-0.08333333333 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + -0.75x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + -0.75x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + -0.75x + x2 = 0 + 0.08333333333
-0.75x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
-0.75x + x2 = 0.08333333333

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 0.08333333333 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.08333333333 + 0.140625

Combine like terms: 0.08333333333 + 0.140625 = 0.22395833333
0.140625 + -0.75x + x2 = 0.22395833333

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.22395833333

Calculate the square root of the right side: 0.473242362

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.473242362 and -0.473242362.

Subproblem 1
x + -0.375 = 0.473242362

Simplifying
x + -0.375 = 0.473242362

Reorder the terms:
-0.375 + x = 0.473242362

Solving
-0.375 + x = 0.473242362

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 0.473242362 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 0.473242362 + 0.375
x = 0.473242362 + 0.375

Combine like terms: 0.473242362 + 0.375 = 0.848242362
x = 0.848242362

Simplifying
x = 0.848242362

Subproblem 2
x + -0.375 = -0.473242362

Simplifying
x + -0.375 = -0.473242362

Reorder the terms:
-0.375 + x = -0.473242362

Solving
-0.375 + x = -0.473242362

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -0.473242362 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -0.473242362 + 0.375
x = -0.473242362 + 0.375

Combine like terms: -0.473242362 + 0.375 = -0.098242362
x = -0.098242362

Simplifying
x = -0.098242362

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.848242362, -0.098242362}