4x(6-8x)(8+9)=-1

Solution for 4x(6-8x)(8+9)=-1 equation:

Simplifying
4x(6 + -8x)(8 + 9) = -1

Combine like terms: 8 + 9 = 17
4x(6 + -8x)(17) = -1

Reorder the terms for easier multiplication:
4 * 17x(6 + -8x) = -1

Multiply 4 * 17
68x(6 + -8x) = -1
(6 * 68x + -8x * 68x) = -1
(408x + -544x2) = -1

Solving
408x + -544x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + 408x + -544x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 408x + -544x2 = 0

Begin completing the square.  Divide all terms by
-544 the coefficient of the squared term: 

Divide each side by '-544'.
-0.001838235294 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.001838235294' to each side of the equation.
-0.001838235294 + -0.75x + 0.001838235294 + x2 = 0 + 0.001838235294

Reorder the terms:
-0.001838235294 + 0.001838235294 + -0.75x + x2 = 0 + 0.001838235294

Combine like terms: -0.001838235294 + 0.001838235294 = 0.000000000000
0.000000000000 + -0.75x + x2 = 0 + 0.001838235294
-0.75x + x2 = 0 + 0.001838235294

Combine like terms: 0 + 0.001838235294 = 0.001838235294
-0.75x + x2 = 0.001838235294

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 = 0.001838235294 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.001838235294 + 0.140625

Combine like terms: 0.001838235294 + 0.140625 = 0.142463235294
0.140625 + -0.75x + x2 = 0.142463235294

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.142463235294

Calculate the square root of the right side: 0.377443023

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.377443023 and -0.377443023.

Subproblem 1
x + -0.375 = 0.377443023

Simplifying
x + -0.375 = 0.377443023

Reorder the terms:
-0.375 + x = 0.377443023

Solving
-0.375 + x = 0.377443023

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 = 0.377443023 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 0.377443023 + 0.375
x = 0.377443023 + 0.375

Combine like terms: 0.377443023 + 0.375 = 0.752443023
x = 0.752443023

Simplifying
x = 0.752443023

Subproblem 2
x + -0.375 = -0.377443023

Simplifying
x + -0.375 = -0.377443023

Reorder the terms:
-0.375 + x = -0.377443023

Solving
-0.375 + x = -0.377443023

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 = -0.377443023 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -0.377443023 + 0.375
x = -0.377443023 + 0.375

Combine like terms: -0.377443023 + 0.375 = -0.002443023
x = -0.002443023

Simplifying
x = -0.002443023

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.752443023, -0.002443023}