3x+[-5-(x+3)]=8x(-5x-9)

Solution for 3x+[-5-(x+3)]=8x(-5x-9) equation:

Simplifying
3x + [-5 + -1(x + 3)] = 8x(-5x + -9)

Reorder the terms:
3x + [-5 + -1(3 + x)] = 8x(-5x + -9)
3x + [-5 + (3 * -1 + x * -1)] = 8x(-5x + -9)
3x + [-5 + (-3 + -1x)] = 8x(-5x + -9)

Combine like terms: -5 + -3 = -8
3x + [-8 + -1x] = 8x(-5x + -9)

Remove brackets around [-8 + -1x]
3x + -8 + -1x = 8x(-5x + -9)

Reorder the terms:
-8 + 3x + -1x = 8x(-5x + -9)

Combine like terms: 3x + -1x = 2x
-8 + 2x = 8x(-5x + -9)

Reorder the terms:
-8 + 2x = 8x(-9 + -5x)
-8 + 2x = (-9 * 8x + -5x * 8x)
-8 + 2x = (-72x + -40x2)

Solving
-8 + 2x = -72x + -40x2

Solving for variable 'x'.

Combine like terms: 2x + 72x = 74x
-8 + 74x + 40x2 = -72x + -40x2 + 72x + 40x2

Reorder the terms:
-8 + 74x + 40x2 = -72x + 72x + -40x2 + 40x2

Combine like terms: -72x + 72x = 0
-8 + 74x + 40x2 = 0 + -40x2 + 40x2
-8 + 74x + 40x2 = -40x2 + 40x2

Combine like terms: -40x2 + 40x2 = 0
-8 + 74x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 37x + 20x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 37x + 20x2)' equal to zero and attempt to solve:

Simplifying
-4 + 37x + 20x2 = 0

Solving
-4 + 37x + 20x2 = 0

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

Divide each side by '20'.
-0.2 + 1.85x + x2 = 0.0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 1.85x + 0.2 + x2 = 0.0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 1.85x + x2 = 0.0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 1.85x + x2 = 0.0 + 0.2
1.85x + x2 = 0.0 + 0.2

Combine like terms: 0.0 + 0.2 = 0.2
1.85x + x2 = 0.2

The x term is 1.85x.  Take half its coefficient (0.925).
Square it (0.855625) and add it to both sides.

Add '0.855625' to each side of the equation.
1.85x + 0.855625 + x2 = 0.2 + 0.855625

Reorder the terms:
0.855625 + 1.85x + x2 = 0.2 + 0.855625

Combine like terms: 0.2 + 0.855625 = 1.055625
0.855625 + 1.85x + x2 = 1.055625

Factor a perfect square on the left side:
(x + 0.925)(x + 0.925) = 1.055625

Calculate the square root of the right side: 1.027436129

Break this problem into two subproblems by setting 
(x + 0.925) equal to 1.027436129 and -1.027436129.

Subproblem 1
x + 0.925 = 1.027436129

Simplifying
x + 0.925 = 1.027436129

Reorder the terms:
0.925 + x = 1.027436129

Solving
0.925 + x = 1.027436129

Solving for variable 'x'.

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

Add '-0.925' to each side of the equation.
0.925 + -0.925 + x = 1.027436129 + -0.925

Combine like terms: 0.925 + -0.925 = 0.000
0.000 + x = 1.027436129 + -0.925
x = 1.027436129 + -0.925

Combine like terms: 1.027436129 + -0.925 = 0.102436129
x = 0.102436129

Simplifying
x = 0.102436129

Subproblem 2
x + 0.925 = -1.027436129

Simplifying
x + 0.925 = -1.027436129

Reorder the terms:
0.925 + x = -1.027436129

Solving
0.925 + x = -1.027436129

Solving for variable 'x'.

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

Add '-0.925' to each side of the equation.
0.925 + -0.925 + x = -1.027436129 + -0.925

Combine like terms: 0.925 + -0.925 = 0.000
0.000 + x = -1.027436129 + -0.925
x = -1.027436129 + -0.925

Combine like terms: -1.027436129 + -0.925 = -1.952436129
x = -1.952436129

Simplifying
x = -1.952436129

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.102436129, -1.952436129}
Solution
x = {0.102436129, -1.952436129}