4x-4-2x-9=3(x+2)(x-4)+5x

Solution for 4x-4-2x-9=3(x+2)(x-4)+5x equation:

Simplifying
4x + -4 + -2x + -9 = 3(x + 2)(x + -4) + 5x

Reorder the terms:
-4 + -9 + 4x + -2x = 3(x + 2)(x + -4) + 5x

Combine like terms: -4 + -9 = -13
-13 + 4x + -2x = 3(x + 2)(x + -4) + 5x

Combine like terms: 4x + -2x = 2x
-13 + 2x = 3(x + 2)(x + -4) + 5x

Reorder the terms:
-13 + 2x = 3(2 + x)(x + -4) + 5x

Reorder the terms:
-13 + 2x = 3(2 + x)(-4 + x) + 5x

Multiply (2 + x) * (-4 + x)
-13 + 2x = 3(2(-4 + x) + x(-4 + x)) + 5x
-13 + 2x = 3((-4 * 2 + x * 2) + x(-4 + x)) + 5x
-13 + 2x = 3((-8 + 2x) + x(-4 + x)) + 5x
-13 + 2x = 3(-8 + 2x + (-4 * x + x * x)) + 5x
-13 + 2x = 3(-8 + 2x + (-4x + x2)) + 5x

Combine like terms: 2x + -4x = -2x
-13 + 2x = 3(-8 + -2x + x2) + 5x
-13 + 2x = (-8 * 3 + -2x * 3 + x2 * 3) + 5x
-13 + 2x = (-24 + -6x + 3x2) + 5x

Reorder the terms:
-13 + 2x = -24 + -6x + 5x + 3x2

Combine like terms: -6x + 5x = -1x
-13 + 2x = -24 + -1x + 3x2

Solving
-13 + 2x = -24 + -1x + 3x2

Solving for variable 'x'.

Reorder the terms:
-13 + 24 + 2x + x + -3x2 = -24 + -1x + 3x2 + 24 + x + -3x2

Combine like terms: -13 + 24 = 11
11 + 2x + x + -3x2 = -24 + -1x + 3x2 + 24 + x + -3x2

Combine like terms: 2x + x = 3x
11 + 3x + -3x2 = -24 + -1x + 3x2 + 24 + x + -3x2

Reorder the terms:
11 + 3x + -3x2 = -24 + 24 + -1x + x + 3x2 + -3x2

Combine like terms: -24 + 24 = 0
11 + 3x + -3x2 = 0 + -1x + x + 3x2 + -3x2
11 + 3x + -3x2 = -1x + x + 3x2 + -3x2

Combine like terms: -1x + x = 0
11 + 3x + -3x2 = 0 + 3x2 + -3x2
11 + 3x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
11 + 3x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-3.666666667 + -1x + x2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + -1x + 3.666666667 + x2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + -1x + x2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + -1x + x2 = 0 + 3.666666667
-1x + x2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
-1x + x2 = 3.666666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 3.666666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 3.666666667 + 0.25

Combine like terms: 3.666666667 + 0.25 = 3.916666667
0.25 + -1x + x2 = 3.916666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3.916666667

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.979057015 and -1.979057015.

Subproblem 1
x + -0.5 = 1.979057015

Simplifying
x + -0.5 = 1.979057015

Reorder the terms:
-0.5 + x = 1.979057015

Solving
-0.5 + x = 1.979057015

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.979057015 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.979057015 + 0.5
x = 1.979057015 + 0.5

Combine like terms: 1.979057015 + 0.5 = 2.479057015
x = 2.479057015

Simplifying
x = 2.479057015

Subproblem 2
x + -0.5 = -1.979057015

Simplifying
x + -0.5 = -1.979057015

Reorder the terms:
-0.5 + x = -1.979057015

Solving
-0.5 + x = -1.979057015

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.979057015 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.979057015 + 0.5
x = -1.979057015 + 0.5

Combine like terms: -1.979057015 + 0.5 = -1.479057015
x = -1.479057015

Simplifying
x = -1.479057015

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.479057015, -1.479057015}