9-(x+5)=(x+1)(3x-2)

Solution for 9-(x+5)=(x+1)(3x-2) equation:

Simplifying
9 + -1(x + 5) = (x + 1)(3x + -2)

Reorder the terms:
9 + -1(5 + x) = (x + 1)(3x + -2)
9 + (5 * -1 + x * -1) = (x + 1)(3x + -2)
9 + (-5 + -1x) = (x + 1)(3x + -2)

Combine like terms: 9 + -5 = 4
4 + -1x = (x + 1)(3x + -2)

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

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

Multiply (1 + x) * (-2 + 3x)
4 + -1x = (1(-2 + 3x) + x(-2 + 3x))
4 + -1x = ((-2 * 1 + 3x * 1) + x(-2 + 3x))
4 + -1x = ((-2 + 3x) + x(-2 + 3x))
4 + -1x = (-2 + 3x + (-2 * x + 3x * x))
4 + -1x = (-2 + 3x + (-2x + 3x2))

Combine like terms: 3x + -2x = 1x
4 + -1x = (-2 + 1x + 3x2)

Solving
4 + -1x = -2 + 1x + 3x2

Solving for variable 'x'.

Reorder the terms:
4 + 2 + -1x + -1x + -3x2 = -2 + 1x + 3x2 + 2 + -1x + -3x2

Combine like terms: 4 + 2 = 6
6 + -1x + -1x + -3x2 = -2 + 1x + 3x2 + 2 + -1x + -3x2

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

Reorder the terms:
6 + -2x + -3x2 = -2 + 2 + 1x + -1x + 3x2 + -3x2

Combine like terms: -2 + 2 = 0
6 + -2x + -3x2 = 0 + 1x + -1x + 3x2 + -3x2
6 + -2x + -3x2 = 1x + -1x + 3x2 + -3x2

Combine like terms: 1x + -1x = 0
6 + -2x + -3x2 = 0 + 3x2 + -3x2
6 + -2x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
6 + -2x + -3x2 = 0

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

Divide each side by '-3'.
-2 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.6666666667x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.6666666667x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.6666666667x + x2 = 0 + 2
0.6666666667x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.6666666667x + x2 = 2

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 = 2 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 2 + 0.1111111112

Combine like terms: 2 + 0.1111111112 = 2.1111111112
0.1111111112 + 0.6666666667x + x2 = 2.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 2.1111111112

Calculate the square root of the right side: 1.452966315

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.452966315 and -1.452966315.

Subproblem 1
x + 0.3333333334 = 1.452966315

Simplifying
x + 0.3333333334 = 1.452966315

Reorder the terms:
0.3333333334 + x = 1.452966315

Solving
0.3333333334 + x = 1.452966315

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 = 1.452966315 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 1.452966315 + -0.3333333334
x = 1.452966315 + -0.3333333334

Combine like terms: 1.452966315 + -0.3333333334 = 1.1196329816
x = 1.1196329816

Simplifying
x = 1.1196329816

Subproblem 2
x + 0.3333333334 = -1.452966315

Simplifying
x + 0.3333333334 = -1.452966315

Reorder the terms:
0.3333333334 + x = -1.452966315

Solving
0.3333333334 + x = -1.452966315

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 = -1.452966315 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -1.452966315 + -0.3333333334
x = -1.452966315 + -0.3333333334

Combine like terms: -1.452966315 + -0.3333333334 = -1.7862996484
x = -1.7862996484

Simplifying
x = -1.7862996484

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1196329816, -1.7862996484}