4x+13=-9+-3(x+9)x-7

Solution for 4x+13=-9+-3(x+9)x-7 equation:

Simplifying
4x + 13 = -9 + -3(x + 9) * x + -7

Reorder the terms:
13 + 4x = -9 + -3(x + 9) * x + -7

Reorder the terms:
13 + 4x = -9 + -3(9 + x) * x + -7

Reorder the terms for easier multiplication:
13 + 4x = -9 + -3x(9 + x) + -7
13 + 4x = -9 + (9 * -3x + x * -3x) + -7
13 + 4x = -9 + (-27x + -3x2) + -7

Reorder the terms:
13 + 4x = -9 + -7 + -27x + -3x2

Combine like terms: -9 + -7 = -16
13 + 4x = -16 + -27x + -3x2

Solving
13 + 4x = -16 + -27x + -3x2

Solving for variable 'x'.

Reorder the terms:
13 + 16 + 4x + 27x + 3x2 = -16 + -27x + -3x2 + 16 + 27x + 3x2

Combine like terms: 13 + 16 = 29
29 + 4x + 27x + 3x2 = -16 + -27x + -3x2 + 16 + 27x + 3x2

Combine like terms: 4x + 27x = 31x
29 + 31x + 3x2 = -16 + -27x + -3x2 + 16 + 27x + 3x2

Reorder the terms:
29 + 31x + 3x2 = -16 + 16 + -27x + 27x + -3x2 + 3x2

Combine like terms: -16 + 16 = 0
29 + 31x + 3x2 = 0 + -27x + 27x + -3x2 + 3x2
29 + 31x + 3x2 = -27x + 27x + -3x2 + 3x2

Combine like terms: -27x + 27x = 0
29 + 31x + 3x2 = 0 + -3x2 + 3x2
29 + 31x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
29 + 31x + 3x2 = 0

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

Divide each side by '3'.
9.666666667 + 10.33333333x + x2 = 0

Move the constant term to the right:

Add '-9.666666667' to each side of the equation.
9.666666667 + 10.33333333x + -9.666666667 + x2 = 0 + -9.666666667

Reorder the terms:
9.666666667 + -9.666666667 + 10.33333333x + x2 = 0 + -9.666666667

Combine like terms: 9.666666667 + -9.666666667 = 0.000000000
0.000000000 + 10.33333333x + x2 = 0 + -9.666666667
10.33333333x + x2 = 0 + -9.666666667

Combine like terms: 0 + -9.666666667 = -9.666666667
10.33333333x + x2 = -9.666666667

The x term is 10.33333333x.  Take half its coefficient (5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
10.33333333x + 26.69444443 + x2 = -9.666666667 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333x + x2 = -9.666666667 + 26.69444443

Combine like terms: -9.666666667 + 26.69444443 = 17.027777763
26.69444443 + 10.33333333x + x2 = 17.027777763

Factor a perfect square on the left side:
(x + 5.166666665)(x + 5.166666665) = 17.027777763

Calculate the square root of the right side: 4.126472799

Break this problem into two subproblems by setting 
(x + 5.166666665) equal to 4.126472799 and -4.126472799.

Subproblem 1
x + 5.166666665 = 4.126472799

Simplifying
x + 5.166666665 = 4.126472799

Reorder the terms:
5.166666665 + x = 4.126472799

Solving
5.166666665 + x = 4.126472799

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = 4.126472799 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = 4.126472799 + -5.166666665
x = 4.126472799 + -5.166666665

Combine like terms: 4.126472799 + -5.166666665 = -1.040193866
x = -1.040193866

Simplifying
x = -1.040193866

Subproblem 2
x + 5.166666665 = -4.126472799

Simplifying
x + 5.166666665 = -4.126472799

Reorder the terms:
5.166666665 + x = -4.126472799

Solving
5.166666665 + x = -4.126472799

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = -4.126472799 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = -4.126472799 + -5.166666665
x = -4.126472799 + -5.166666665

Combine like terms: -4.126472799 + -5.166666665 = -9.293139464
x = -9.293139464

Simplifying
x = -9.293139464

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.040193866, -9.293139464}