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

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

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

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

Combine like terms: -5x + -1x = -6x
3x(-3 + -6x) = 8x + (-5x + -9)
(-3 * 3x + -6x * 3x) = 8x + (-5x + -9)
(-9x + -18x2) = 8x + (-5x + -9)

Reorder the terms:
-9x + -18x2 = 8x + (-9 + -5x)

Remove parenthesis around (-9 + -5x)
-9x + -18x2 = 8x + -9 + -5x

Reorder the terms:
-9x + -18x2 = -9 + 8x + -5x

Combine like terms: 8x + -5x = 3x
-9x + -18x2 = -9 + 3x

Solving
-9x + -18x2 = -9 + 3x

Solving for variable 'x'.

Reorder the terms:
9 + -9x + -3x + -18x2 = -9 + 3x + 9 + -3x

Combine like terms: -9x + -3x = -12x
9 + -12x + -18x2 = -9 + 3x + 9 + -3x

Reorder the terms:
9 + -12x + -18x2 = -9 + 9 + 3x + -3x

Combine like terms: -9 + 9 = 0
9 + -12x + -18x2 = 0 + 3x + -3x
9 + -12x + -18x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
9 + -12x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -4x + -6x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -4x + -6x2)' equal to zero and attempt to solve:

Simplifying
3 + -4x + -6x2 = 0

Solving
3 + -4x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.5 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.6666666667x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.6666666667x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.6666666667x + x2 = 0 + 0.5
0.6666666667x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.6666666667x + x2 = 0.5

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 0.5 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.5 + 0.1111111112

Combine like terms: 0.5 + 0.1111111112 = 0.6111111112
0.1111111112 + 0.6666666667x + x2 = 0.6111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.6111111112

Calculate the square root of the right side: 0.78173596

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.78173596 and -0.78173596.

Subproblem 1
x + 0.3333333334 = 0.78173596

Simplifying
x + 0.3333333334 = 0.78173596

Reorder the terms:
0.3333333334 + x = 0.78173596

Solving
0.3333333334 + x = 0.78173596

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.78173596 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.78173596 + -0.3333333334
x = 0.78173596 + -0.3333333334

Combine like terms: 0.78173596 + -0.3333333334 = 0.4484026266
x = 0.4484026266

Simplifying
x = 0.4484026266

Subproblem 2
x + 0.3333333334 = -0.78173596

Simplifying
x + 0.3333333334 = -0.78173596

Reorder the terms:
0.3333333334 + x = -0.78173596

Solving
0.3333333334 + x = -0.78173596

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.78173596 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.78173596 + -0.3333333334
x = -0.78173596 + -0.3333333334

Combine like terms: -0.78173596 + -0.3333333334 = -1.1150692934
x = -1.1150692934

Simplifying
x = -1.1150692934

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4484026266, -1.1150692934}
Solution
x = {0.4484026266, -1.1150692934}