(2x+9)(8x-1)=(4x+5)2

Solution for (2x+9)(8x-1)=(4x+5)2 equation:

Simplifying
(2x + 9)(8x + -1) = (4x + 5) * 2

Reorder the terms:
(9 + 2x)(8x + -1) = (4x + 5) * 2

Reorder the terms:
(9 + 2x)(-1 + 8x) = (4x + 5) * 2

Multiply (9 + 2x) * (-1 + 8x)
(9(-1 + 8x) + 2x * (-1 + 8x)) = (4x + 5) * 2
((-1 * 9 + 8x * 9) + 2x * (-1 + 8x)) = (4x + 5) * 2
((-9 + 72x) + 2x * (-1 + 8x)) = (4x + 5) * 2
(-9 + 72x + (-1 * 2x + 8x * 2x)) = (4x + 5) * 2
(-9 + 72x + (-2x + 16x2)) = (4x + 5) * 2

Combine like terms: 72x + -2x = 70x
(-9 + 70x + 16x2) = (4x + 5) * 2

Reorder the terms:
-9 + 70x + 16x2 = (5 + 4x) * 2

Reorder the terms for easier multiplication:
-9 + 70x + 16x2 = 2(5 + 4x)
-9 + 70x + 16x2 = (5 * 2 + 4x * 2)
-9 + 70x + 16x2 = (10 + 8x)

Solving
-9 + 70x + 16x2 = 10 + 8x

Solving for variable 'x'.

Reorder the terms:
-9 + -10 + 70x + -8x + 16x2 = 10 + 8x + -10 + -8x

Combine like terms: -9 + -10 = -19
-19 + 70x + -8x + 16x2 = 10 + 8x + -10 + -8x

Combine like terms: 70x + -8x = 62x
-19 + 62x + 16x2 = 10 + 8x + -10 + -8x

Reorder the terms:
-19 + 62x + 16x2 = 10 + -10 + 8x + -8x

Combine like terms: 10 + -10 = 0
-19 + 62x + 16x2 = 0 + 8x + -8x
-19 + 62x + 16x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-19 + 62x + 16x2 = 0

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

Divide each side by '16'.
-1.1875 + 3.875x + x2 = 0

Move the constant term to the right:

Add '1.1875' to each side of the equation.
-1.1875 + 3.875x + 1.1875 + x2 = 0 + 1.1875

Reorder the terms:
-1.1875 + 1.1875 + 3.875x + x2 = 0 + 1.1875

Combine like terms: -1.1875 + 1.1875 = 0.0000
0.0000 + 3.875x + x2 = 0 + 1.1875
3.875x + x2 = 0 + 1.1875

Combine like terms: 0 + 1.1875 = 1.1875
3.875x + x2 = 1.1875

The x term is 3.875x.  Take half its coefficient (1.9375).
Square it (3.75390625) and add it to both sides.

Add '3.75390625' to each side of the equation.
3.875x + 3.75390625 + x2 = 1.1875 + 3.75390625

Reorder the terms:
3.75390625 + 3.875x + x2 = 1.1875 + 3.75390625

Combine like terms: 1.1875 + 3.75390625 = 4.94140625
3.75390625 + 3.875x + x2 = 4.94140625

Factor a perfect square on the left side:
(x + 1.9375)(x + 1.9375) = 4.94140625

Calculate the square root of the right side: 2.222927405

Break this problem into two subproblems by setting 
(x + 1.9375) equal to 2.222927405 and -2.222927405.

Subproblem 1
x + 1.9375 = 2.222927405

Simplifying
x + 1.9375 = 2.222927405

Reorder the terms:
1.9375 + x = 2.222927405

Solving
1.9375 + x = 2.222927405

Solving for variable 'x'.

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

Add '-1.9375' to each side of the equation.
1.9375 + -1.9375 + x = 2.222927405 + -1.9375

Combine like terms: 1.9375 + -1.9375 = 0.0000
0.0000 + x = 2.222927405 + -1.9375
x = 2.222927405 + -1.9375

Combine like terms: 2.222927405 + -1.9375 = 0.285427405
x = 0.285427405

Simplifying
x = 0.285427405

Subproblem 2
x + 1.9375 = -2.222927405

Simplifying
x + 1.9375 = -2.222927405

Reorder the terms:
1.9375 + x = -2.222927405

Solving
1.9375 + x = -2.222927405

Solving for variable 'x'.

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

Add '-1.9375' to each side of the equation.
1.9375 + -1.9375 + x = -2.222927405 + -1.9375

Combine like terms: 1.9375 + -1.9375 = 0.0000
0.0000 + x = -2.222927405 + -1.9375
x = -2.222927405 + -1.9375

Combine like terms: -2.222927405 + -1.9375 = -4.160427405
x = -4.160427405

Simplifying
x = -4.160427405

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.285427405, -4.160427405}