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

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

Simplifying
(9x + -4)(9x + 1) = 8x + -1

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

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

Multiply (-4 + 9x) * (1 + 9x)
(-4(1 + 9x) + 9x * (1 + 9x)) = 8x + -1
((1 * -4 + 9x * -4) + 9x * (1 + 9x)) = 8x + -1
((-4 + -36x) + 9x * (1 + 9x)) = 8x + -1
(-4 + -36x + (1 * 9x + 9x * 9x)) = 8x + -1
(-4 + -36x + (9x + 81x2)) = 8x + -1

Combine like terms: -36x + 9x = -27x
(-4 + -27x + 81x2) = 8x + -1

Reorder the terms:
-4 + -27x + 81x2 = -1 + 8x

Solving
-4 + -27x + 81x2 = -1 + 8x

Solving for variable 'x'.

Reorder the terms:
-4 + 1 + -27x + -8x + 81x2 = -1 + 8x + 1 + -8x

Combine like terms: -4 + 1 = -3
-3 + -27x + -8x + 81x2 = -1 + 8x + 1 + -8x

Combine like terms: -27x + -8x = -35x
-3 + -35x + 81x2 = -1 + 8x + 1 + -8x

Reorder the terms:
-3 + -35x + 81x2 = -1 + 1 + 8x + -8x

Combine like terms: -1 + 1 = 0
-3 + -35x + 81x2 = 0 + 8x + -8x
-3 + -35x + 81x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-3 + -35x + 81x2 = 0

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

Divide each side by '81'.
-0.03703703704 + -0.4320987654x + x2 = 0

Move the constant term to the right:

Add '0.03703703704' to each side of the equation.
-0.03703703704 + -0.4320987654x + 0.03703703704 + x2 = 0 + 0.03703703704

Reorder the terms:
-0.03703703704 + 0.03703703704 + -0.4320987654x + x2 = 0 + 0.03703703704

Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000
0.00000000000 + -0.4320987654x + x2 = 0 + 0.03703703704
-0.4320987654x + x2 = 0 + 0.03703703704

Combine like terms: 0 + 0.03703703704 = 0.03703703704
-0.4320987654x + x2 = 0.03703703704

The x term is -0.4320987654x.  Take half its coefficient (-0.2160493827).
Square it (0.04667733577) and add it to both sides.

Add '0.04667733577' to each side of the equation.
-0.4320987654x + 0.04667733577 + x2 = 0.03703703704 + 0.04667733577

Reorder the terms:
0.04667733577 + -0.4320987654x + x2 = 0.03703703704 + 0.04667733577

Combine like terms: 0.03703703704 + 0.04667733577 = 0.08371437281
0.04667733577 + -0.4320987654x + x2 = 0.08371437281

Factor a perfect square on the left side:
(x + -0.2160493827)(x + -0.2160493827) = 0.08371437281

Calculate the square root of the right side: 0.289334362

Break this problem into two subproblems by setting 
(x + -0.2160493827) equal to 0.289334362 and -0.289334362.

Subproblem 1
x + -0.2160493827 = 0.289334362

Simplifying
x + -0.2160493827 = 0.289334362

Reorder the terms:
-0.2160493827 + x = 0.289334362

Solving
-0.2160493827 + x = 0.289334362

Solving for variable 'x'.

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

Add '0.2160493827' to each side of the equation.
-0.2160493827 + 0.2160493827 + x = 0.289334362 + 0.2160493827

Combine like terms: -0.2160493827 + 0.2160493827 = 0.0000000000
0.0000000000 + x = 0.289334362 + 0.2160493827
x = 0.289334362 + 0.2160493827

Combine like terms: 0.289334362 + 0.2160493827 = 0.5053837447
x = 0.5053837447

Simplifying
x = 0.5053837447

Subproblem 2
x + -0.2160493827 = -0.289334362

Simplifying
x + -0.2160493827 = -0.289334362

Reorder the terms:
-0.2160493827 + x = -0.289334362

Solving
-0.2160493827 + x = -0.289334362

Solving for variable 'x'.

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

Add '0.2160493827' to each side of the equation.
-0.2160493827 + 0.2160493827 + x = -0.289334362 + 0.2160493827

Combine like terms: -0.2160493827 + 0.2160493827 = 0.0000000000
0.0000000000 + x = -0.289334362 + 0.2160493827
x = -0.289334362 + 0.2160493827

Combine like terms: -0.289334362 + 0.2160493827 = -0.0732849793
x = -0.0732849793

Simplifying
x = -0.0732849793

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5053837447, -0.0732849793}