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

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

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

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

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

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

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

Solving
-1 + 6x + 16x2 = 5x

Solving for variable 'x'.

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

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

Combine like terms: 5x + -5x = 0
-1 + 1x + 16x2 = 0

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

Divide each side by '16'.
-0.0625 + 0.0625x + x2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + 0.0625x + 0.0625 + x2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + 0.0625x + x2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + 0.0625x + x2 = 0 + 0.0625
0.0625x + x2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
0.0625x + x2 = 0.0625

The x term is 0.0625x.  Take half its coefficient (0.03125).
Square it (0.0009765625) and add it to both sides.

Add '0.0009765625' to each side of the equation.
0.0625x + 0.0009765625 + x2 = 0.0625 + 0.0009765625

Reorder the terms:
0.0009765625 + 0.0625x + x2 = 0.0625 + 0.0009765625

Combine like terms: 0.0625 + 0.0009765625 = 0.0634765625
0.0009765625 + 0.0625x + x2 = 0.0634765625

Factor a perfect square on the left side:
(x + 0.03125)(x + 0.03125) = 0.0634765625

Calculate the square root of the right side: 0.251945555

Break this problem into two subproblems by setting 
(x + 0.03125) equal to 0.251945555 and -0.251945555.

Subproblem 1
x + 0.03125 = 0.251945555

Simplifying
x + 0.03125 = 0.251945555

Reorder the terms:
0.03125 + x = 0.251945555

Solving
0.03125 + x = 0.251945555

Solving for variable 'x'.

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

Add '-0.03125' to each side of the equation.
0.03125 + -0.03125 + x = 0.251945555 + -0.03125

Combine like terms: 0.03125 + -0.03125 = 0.00000
0.00000 + x = 0.251945555 + -0.03125
x = 0.251945555 + -0.03125

Combine like terms: 0.251945555 + -0.03125 = 0.220695555
x = 0.220695555

Simplifying
x = 0.220695555

Subproblem 2
x + 0.03125 = -0.251945555

Simplifying
x + 0.03125 = -0.251945555

Reorder the terms:
0.03125 + x = -0.251945555

Solving
0.03125 + x = -0.251945555

Solving for variable 'x'.

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

Add '-0.03125' to each side of the equation.
0.03125 + -0.03125 + x = -0.251945555 + -0.03125

Combine like terms: 0.03125 + -0.03125 = 0.00000
0.00000 + x = -0.251945555 + -0.03125
x = -0.251945555 + -0.03125

Combine like terms: -0.251945555 + -0.03125 = -0.283195555
x = -0.283195555

Simplifying
x = -0.283195555

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.220695555, -0.283195555}