(8x-1)(2x+1)=5

Solution for (8x-1)(2x+1)=5 equation:

Simplifying
(8x + -1)(2x + 1) = 5

Reorder the terms:
(-1 + 8x)(2x + 1) = 5

Reorder the terms:
(-1 + 8x)(1 + 2x) = 5

Multiply (-1 + 8x) * (1 + 2x)
(-1(1 + 2x) + 8x * (1 + 2x)) = 5
((1 * -1 + 2x * -1) + 8x * (1 + 2x)) = 5
((-1 + -2x) + 8x * (1 + 2x)) = 5
(-1 + -2x + (1 * 8x + 2x * 8x)) = 5
(-1 + -2x + (8x + 16x2)) = 5

Combine like terms: -2x + 8x = 6x
(-1 + 6x + 16x2) = 5

Solving
-1 + 6x + 16x2 = 5

Solving for variable 'x'.

Reorder the terms:
-1 + -5 + 6x + 16x2 = 5 + -5

Combine like terms: -1 + -5 = -6
-6 + 6x + 16x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-6 + 6x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 3x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 3x + 8x2)' equal to zero and attempt to solve:

Simplifying
-3 + 3x + 8x2 = 0

Solving
-3 + 3x + 8x2 = 0

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

Divide each side by '8'.
-0.375 + 0.375x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + 0.375x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + 0.375x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + 0.375x + x2 = 0 + 0.375
0.375x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
0.375x + x2 = 0.375

The x term is 0.375x.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375x + 0.03515625 + x2 = 0.375 + 0.03515625

Reorder the terms:
0.03515625 + 0.375x + x2 = 0.375 + 0.03515625

Combine like terms: 0.375 + 0.03515625 = 0.41015625
0.03515625 + 0.375x + x2 = 0.41015625

Factor a perfect square on the left side:
(x + 0.1875)(x + 0.1875) = 0.41015625

Calculate the square root of the right side: 0.640434423

Break this problem into two subproblems by setting 
(x + 0.1875) equal to 0.640434423 and -0.640434423.

Subproblem 1
x + 0.1875 = 0.640434423

Simplifying
x + 0.1875 = 0.640434423

Reorder the terms:
0.1875 + x = 0.640434423

Solving
0.1875 + x = 0.640434423

Solving for variable 'x'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + x = 0.640434423 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + x = 0.640434423 + -0.1875
x = 0.640434423 + -0.1875

Combine like terms: 0.640434423 + -0.1875 = 0.452934423
x = 0.452934423

Simplifying
x = 0.452934423

Subproblem 2
x + 0.1875 = -0.640434423

Simplifying
x + 0.1875 = -0.640434423

Reorder the terms:
0.1875 + x = -0.640434423

Solving
0.1875 + x = -0.640434423

Solving for variable 'x'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + x = -0.640434423 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + x = -0.640434423 + -0.1875
x = -0.640434423 + -0.1875

Combine like terms: -0.640434423 + -0.1875 = -0.827934423
x = -0.827934423

Simplifying
x = -0.827934423

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.452934423, -0.827934423}
Solution
x = {0.452934423, -0.827934423}