3x*3x-2x-1=2x+3

Solution for 3x*3x-2x-1=2x+3 equation:

Simplifying
3x * 3x + -2x + -1 = 2x + 3

Reorder the terms for easier multiplication:
3 * 3x * x + -2x + -1 = 2x + 3

Multiply 3 * 3
9x * x + -2x + -1 = 2x + 3

Multiply x * x
9x2 + -2x + -1 = 2x + 3

Reorder the terms:
-1 + -2x + 9x2 = 2x + 3

Reorder the terms:
-1 + -2x + 9x2 = 3 + 2x

Solving
-1 + -2x + 9x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
-1 + -3 + -2x + -2x + 9x2 = 3 + 2x + -3 + -2x

Combine like terms: -1 + -3 = -4
-4 + -2x + -2x + 9x2 = 3 + 2x + -3 + -2x

Combine like terms: -2x + -2x = -4x
-4 + -4x + 9x2 = 3 + 2x + -3 + -2x

Reorder the terms:
-4 + -4x + 9x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
-4 + -4x + 9x2 = 0 + 2x + -2x
-4 + -4x + 9x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-4 + -4x + 9x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

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 = 0.4444444444 + 0.04938271604

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

Combine like terms: 0.4444444444 + 0.04938271604 = 0.49382716044
0.04938271604 + -0.4444444444x + x2 = 0.49382716044

Factor a perfect square on the left side:
(x + -0.2222222222)(x + -0.2222222222) = 0.49382716044

Calculate the square root of the right side: 0.702728369

Break this problem into two subproblems by setting 
(x + -0.2222222222) equal to 0.702728369 and -0.702728369.

Subproblem 1
x + -0.2222222222 = 0.702728369

Simplifying
x + -0.2222222222 = 0.702728369

Reorder the terms:
-0.2222222222 + x = 0.702728369

Solving
-0.2222222222 + x = 0.702728369

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 = 0.702728369 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x = 0.702728369 + 0.2222222222
x = 0.702728369 + 0.2222222222

Combine like terms: 0.702728369 + 0.2222222222 = 0.9249505912
x = 0.9249505912

Simplifying
x = 0.9249505912

Subproblem 2
x + -0.2222222222 = -0.702728369

Simplifying
x + -0.2222222222 = -0.702728369

Reorder the terms:
-0.2222222222 + x = -0.702728369

Solving
-0.2222222222 + x = -0.702728369

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 = -0.702728369 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x = -0.702728369 + 0.2222222222
x = -0.702728369 + 0.2222222222

Combine like terms: -0.702728369 + 0.2222222222 = -0.4805061468
x = -0.4805061468

Simplifying
x = -0.4805061468

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9249505912, -0.4805061468}