9x(x+3)-6=23x-5

Solution for 9x(x+3)-6=23x-5 equation:

Simplifying
9x(x + 3) + -6 = 23x + -5

Reorder the terms:
9x(3 + x) + -6 = 23x + -5
(3 * 9x + x * 9x) + -6 = 23x + -5
(27x + 9x2) + -6 = 23x + -5

Reorder the terms:
-6 + 27x + 9x2 = 23x + -5

Reorder the terms:
-6 + 27x + 9x2 = -5 + 23x

Solving
-6 + 27x + 9x2 = -5 + 23x

Solving for variable 'x'.

Reorder the terms:
-6 + 5 + 27x + -23x + 9x2 = -5 + 23x + 5 + -23x

Combine like terms: -6 + 5 = -1
-1 + 27x + -23x + 9x2 = -5 + 23x + 5 + -23x

Combine like terms: 27x + -23x = 4x
-1 + 4x + 9x2 = -5 + 23x + 5 + -23x

Reorder the terms:
-1 + 4x + 9x2 = -5 + 5 + 23x + -23x

Combine like terms: -5 + 5 = 0
-1 + 4x + 9x2 = 0 + 23x + -23x
-1 + 4x + 9x2 = 23x + -23x

Combine like terms: 23x + -23x = 0
-1 + 4x + 9x2 = 0

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

Divide each side by '9'.
-0.1111111111 + 0.4444444444x + x2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.4444444444x + 0.1111111111 + x2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + 0.4444444444x + x2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + 0.4444444444x + x2 = 0 + 0.1111111111
0.4444444444x + x2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
0.4444444444x + x2 = 0.1111111111

The x term is 0.4444444444x.  Take half its coefficient (0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
0.4444444444x + 0.04938271604 + x2 = 0.1111111111 + 0.04938271604

Reorder the terms:
0.04938271604 + 0.4444444444x + x2 = 0.1111111111 + 0.04938271604

Combine like terms: 0.1111111111 + 0.04938271604 = 0.16049382714
0.04938271604 + 0.4444444444x + x2 = 0.16049382714

Factor a perfect square on the left side:
(x + 0.2222222222)(x + 0.2222222222) = 0.16049382714

Calculate the square root of the right side: 0.400616808

Break this problem into two subproblems by setting 
(x + 0.2222222222) equal to 0.400616808 and -0.400616808.

Subproblem 1
x + 0.2222222222 = 0.400616808

Simplifying
x + 0.2222222222 = 0.400616808

Reorder the terms:
0.2222222222 + x = 0.400616808

Solving
0.2222222222 + x = 0.400616808

Solving for variable 'x'.

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

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -0.2222222222 + x = 0.400616808 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + x = 0.400616808 + -0.2222222222
x = 0.400616808 + -0.2222222222

Combine like terms: 0.400616808 + -0.2222222222 = 0.1783945858
x = 0.1783945858

Simplifying
x = 0.1783945858

Subproblem 2
x + 0.2222222222 = -0.400616808

Simplifying
x + 0.2222222222 = -0.400616808

Reorder the terms:
0.2222222222 + x = -0.400616808

Solving
0.2222222222 + x = -0.400616808

Solving for variable 'x'.

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

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -0.2222222222 + x = -0.400616808 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + x = -0.400616808 + -0.2222222222
x = -0.400616808 + -0.2222222222

Combine like terms: -0.400616808 + -0.2222222222 = -0.6228390302
x = -0.6228390302

Simplifying
x = -0.6228390302

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1783945858, -0.6228390302}