52=(4x+1)(x-1)

Solution for 52=(4x+1)(x-1) equation:

Simplifying
52 = (4x + 1)(x + -1)

Reorder the terms:
52 = (1 + 4x)(x + -1)

Reorder the terms:
52 = (1 + 4x)(-1 + x)

Multiply (1 + 4x) * (-1 + x)
52 = (1(-1 + x) + 4x * (-1 + x))
52 = ((-1 * 1 + x * 1) + 4x * (-1 + x))
52 = ((-1 + 1x) + 4x * (-1 + x))
52 = (-1 + 1x + (-1 * 4x + x * 4x))
52 = (-1 + 1x + (-4x + 4x2))

Combine like terms: 1x + -4x = -3x
52 = (-1 + -3x + 4x2)

Solving
52 = -1 + -3x + 4x2

Solving for variable 'x'.

Combine like terms: 52 + 1 = 53
53 + 3x + -4x2 = -1 + -3x + 4x2 + 1 + 3x + -4x2

Reorder the terms:
53 + 3x + -4x2 = -1 + 1 + -3x + 3x + 4x2 + -4x2

Combine like terms: -1 + 1 = 0
53 + 3x + -4x2 = 0 + -3x + 3x + 4x2 + -4x2
53 + 3x + -4x2 = -3x + 3x + 4x2 + -4x2

Combine like terms: -3x + 3x = 0
53 + 3x + -4x2 = 0 + 4x2 + -4x2
53 + 3x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
53 + 3x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-13.25 + -0.75x + x2 = 0

Move the constant term to the right:

Add '13.25' to each side of the equation.
-13.25 + -0.75x + 13.25 + x2 = 0 + 13.25

Reorder the terms:
-13.25 + 13.25 + -0.75x + x2 = 0 + 13.25

Combine like terms: -13.25 + 13.25 = 0.00
0.00 + -0.75x + x2 = 0 + 13.25
-0.75x + x2 = 0 + 13.25

Combine like terms: 0 + 13.25 = 13.25
-0.75x + x2 = 13.25

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 = 13.25 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 13.25 + 0.140625

Combine like terms: 13.25 + 0.140625 = 13.390625
0.140625 + -0.75x + x2 = 13.390625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 13.390625

Calculate the square root of the right side: 3.659320292

Break this problem into two subproblems by setting 
(x + -0.375) equal to 3.659320292 and -3.659320292.

Subproblem 1
x + -0.375 = 3.659320292

Simplifying
x + -0.375 = 3.659320292

Reorder the terms:
-0.375 + x = 3.659320292

Solving
-0.375 + x = 3.659320292

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 = 3.659320292 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 3.659320292 + 0.375
x = 3.659320292 + 0.375

Combine like terms: 3.659320292 + 0.375 = 4.034320292
x = 4.034320292

Simplifying
x = 4.034320292

Subproblem 2
x + -0.375 = -3.659320292

Simplifying
x + -0.375 = -3.659320292

Reorder the terms:
-0.375 + x = -3.659320292

Solving
-0.375 + x = -3.659320292

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 = -3.659320292 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -3.659320292 + 0.375
x = -3.659320292 + 0.375

Combine like terms: -3.659320292 + 0.375 = -3.284320292
x = -3.284320292

Simplifying
x = -3.284320292

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.034320292, -3.284320292}