5(4x-4)3(8-3x)-5(2x+4)=-1

Solution for 5(4x-4)3(8-3x)-5(2x+4)=-1 equation:

Simplifying
5(4x + -4) * 3(8 + -3x) + -5(2x + 4) = -1

Reorder the terms:
5(-4 + 4x) * 3(8 + -3x) + -5(2x + 4) = -1

Reorder the terms for easier multiplication:
5 * 3(-4 + 4x)(8 + -3x) + -5(2x + 4) = -1

Multiply 5 * 3
15(-4 + 4x)(8 + -3x) + -5(2x + 4) = -1

Multiply (-4 + 4x) * (8 + -3x)
15(-4(8 + -3x) + 4x * (8 + -3x)) + -5(2x + 4) = -1
15((8 * -4 + -3x * -4) + 4x * (8 + -3x)) + -5(2x + 4) = -1
15((-32 + 12x) + 4x * (8 + -3x)) + -5(2x + 4) = -1
15(-32 + 12x + (8 * 4x + -3x * 4x)) + -5(2x + 4) = -1
15(-32 + 12x + (32x + -12x2)) + -5(2x + 4) = -1

Combine like terms: 12x + 32x = 44x
15(-32 + 44x + -12x2) + -5(2x + 4) = -1
(-32 * 15 + 44x * 15 + -12x2 * 15) + -5(2x + 4) = -1
(-480 + 660x + -180x2) + -5(2x + 4) = -1

Reorder the terms:
-480 + 660x + -180x2 + -5(4 + 2x) = -1
-480 + 660x + -180x2 + (4 * -5 + 2x * -5) = -1
-480 + 660x + -180x2 + (-20 + -10x) = -1

Reorder the terms:
-480 + -20 + 660x + -10x + -180x2 = -1

Combine like terms: -480 + -20 = -500
-500 + 660x + -10x + -180x2 = -1

Combine like terms: 660x + -10x = 650x
-500 + 650x + -180x2 = -1

Solving
-500 + 650x + -180x2 = -1

Solving for variable 'x'.

Reorder the terms:
-500 + 1 + 650x + -180x2 = -1 + 1

Combine like terms: -500 + 1 = -499
-499 + 650x + -180x2 = -1 + 1

Combine like terms: -1 + 1 = 0
-499 + 650x + -180x2 = 0

Begin completing the square.  Divide all terms by
-180 the coefficient of the squared term: 

Divide each side by '-180'.
2.772222222 + -3.611111111x + x2 = 0.0

Move the constant term to the right:

Add '-2.772222222' to each side of the equation.
2.772222222 + -3.611111111x + -2.772222222 + x2 = 0.0 + -2.772222222

Reorder the terms:
2.772222222 + -2.772222222 + -3.611111111x + x2 = 0.0 + -2.772222222

Combine like terms: 2.772222222 + -2.772222222 = 0.000000000
0.000000000 + -3.611111111x + x2 = 0.0 + -2.772222222
-3.611111111x + x2 = 0.0 + -2.772222222

Combine like terms: 0.0 + -2.772222222 = -2.772222222
-3.611111111x + x2 = -2.772222222

The x term is -3.611111111x.  Take half its coefficient (-1.805555556).
Square it (3.260030866) and add it to both sides.

Add '3.260030866' to each side of the equation.
-3.611111111x + 3.260030866 + x2 = -2.772222222 + 3.260030866

Reorder the terms:
3.260030866 + -3.611111111x + x2 = -2.772222222 + 3.260030866

Combine like terms: -2.772222222 + 3.260030866 = 0.487808644
3.260030866 + -3.611111111x + x2 = 0.487808644

Factor a perfect square on the left side:
(x + -1.805555556)(x + -1.805555556) = 0.487808644

Calculate the square root of the right side: 0.698432992

Break this problem into two subproblems by setting 
(x + -1.805555556) equal to 0.698432992 and -0.698432992.

Subproblem 1
x + -1.805555556 = 0.698432992

Simplifying
x + -1.805555556 = 0.698432992

Reorder the terms:
-1.805555556 + x = 0.698432992

Solving
-1.805555556 + x = 0.698432992

Solving for variable 'x'.

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

Add '1.805555556' to each side of the equation.
-1.805555556 + 1.805555556 + x = 0.698432992 + 1.805555556

Combine like terms: -1.805555556 + 1.805555556 = 0.000000000
0.000000000 + x = 0.698432992 + 1.805555556
x = 0.698432992 + 1.805555556

Combine like terms: 0.698432992 + 1.805555556 = 2.503988548
x = 2.503988548

Simplifying
x = 2.503988548

Subproblem 2
x + -1.805555556 = -0.698432992

Simplifying
x + -1.805555556 = -0.698432992

Reorder the terms:
-1.805555556 + x = -0.698432992

Solving
-1.805555556 + x = -0.698432992

Solving for variable 'x'.

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

Add '1.805555556' to each side of the equation.
-1.805555556 + 1.805555556 + x = -0.698432992 + 1.805555556

Combine like terms: -1.805555556 + 1.805555556 = 0.000000000
0.000000000 + x = -0.698432992 + 1.805555556
x = -0.698432992 + 1.805555556

Combine like terms: -0.698432992 + 1.805555556 = 1.107122564
x = 1.107122564

Simplifying
x = 1.107122564

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.503988548, 1.107122564}