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

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

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

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

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

Multiply (-1 + 4x) * (3 + 2x)
(-1(3 + 2x) + 4x * (3 + 2x)) = (x + 1)(x + -1)
((3 * -1 + 2x * -1) + 4x * (3 + 2x)) = (x + 1)(x + -1)
((-3 + -2x) + 4x * (3 + 2x)) = (x + 1)(x + -1)
(-3 + -2x + (3 * 4x + 2x * 4x)) = (x + 1)(x + -1)
(-3 + -2x + (12x + 8x2)) = (x + 1)(x + -1)

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

Reorder the terms:
-3 + 10x + 8x2 = (1 + x)(x + -1)

Reorder the terms:
-3 + 10x + 8x2 = (1 + x)(-1 + x)

Multiply (1 + x) * (-1 + x)
-3 + 10x + 8x2 = (1(-1 + x) + x(-1 + x))
-3 + 10x + 8x2 = ((-1 * 1 + x * 1) + x(-1 + x))
-3 + 10x + 8x2 = ((-1 + 1x) + x(-1 + x))
-3 + 10x + 8x2 = (-1 + 1x + (-1 * x + x * x))
-3 + 10x + 8x2 = (-1 + 1x + (-1x + x2))

Combine like terms: 1x + -1x = 0
-3 + 10x + 8x2 = (-1 + 0 + x2)
-3 + 10x + 8x2 = (-1 + x2)

Solving
-3 + 10x + 8x2 = -1 + x2

Solving for variable 'x'.

Reorder the terms:
-3 + 1 + 10x + 8x2 + -1x2 = -1 + x2 + 1 + -1x2

Combine like terms: -3 + 1 = -2
-2 + 10x + 8x2 + -1x2 = -1 + x2 + 1 + -1x2

Combine like terms: 8x2 + -1x2 = 7x2
-2 + 10x + 7x2 = -1 + x2 + 1 + -1x2

Reorder the terms:
-2 + 10x + 7x2 = -1 + 1 + x2 + -1x2

Combine like terms: -1 + 1 = 0
-2 + 10x + 7x2 = 0 + x2 + -1x2
-2 + 10x + 7x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 10x + 7x2 = 0

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

Divide each side by '7'.
-0.2857142857 + 1.428571429x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 1.428571429x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + 1.428571429x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + 1.428571429x + x2 = 0 + 0.2857142857
1.428571429x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
1.428571429x + x2 = 0.2857142857

The x term is 1.428571429x.  Take half its coefficient (0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
1.428571429x + 0.5102040819 + x2 = 0.2857142857 + 0.5102040819

Reorder the terms:
0.5102040819 + 1.428571429x + x2 = 0.2857142857 + 0.5102040819

Combine like terms: 0.2857142857 + 0.5102040819 = 0.7959183676
0.5102040819 + 1.428571429x + x2 = 0.7959183676

Factor a perfect square on the left side:
(x + 0.7142857145)(x + 0.7142857145) = 0.7959183676

Calculate the square root of the right side: 0.892142571

Break this problem into two subproblems by setting 
(x + 0.7142857145) equal to 0.892142571 and -0.892142571.

Subproblem 1
x + 0.7142857145 = 0.892142571

Simplifying
x + 0.7142857145 = 0.892142571

Reorder the terms:
0.7142857145 + x = 0.892142571

Solving
0.7142857145 + x = 0.892142571

Solving for variable 'x'.

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

Add '-0.7142857145' to each side of the equation.
0.7142857145 + -0.7142857145 + x = 0.892142571 + -0.7142857145

Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000
0.0000000000 + x = 0.892142571 + -0.7142857145
x = 0.892142571 + -0.7142857145

Combine like terms: 0.892142571 + -0.7142857145 = 0.1778568565
x = 0.1778568565

Simplifying
x = 0.1778568565

Subproblem 2
x + 0.7142857145 = -0.892142571

Simplifying
x + 0.7142857145 = -0.892142571

Reorder the terms:
0.7142857145 + x = -0.892142571

Solving
0.7142857145 + x = -0.892142571

Solving for variable 'x'.

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

Add '-0.7142857145' to each side of the equation.
0.7142857145 + -0.7142857145 + x = -0.892142571 + -0.7142857145

Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000
0.0000000000 + x = -0.892142571 + -0.7142857145
x = -0.892142571 + -0.7142857145

Combine like terms: -0.892142571 + -0.7142857145 = -1.6064282855
x = -1.6064282855

Simplifying
x = -1.6064282855

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1778568565, -1.6064282855}