2x-1+3x+1=18x^2-3x-3

Solution for 2x-1+3x+1=18x^2-3x-3 equation:

Simplifying
2x + -1 + 3x + 1 = 18x2 + -3x + -3

Reorder the terms:
-1 + 1 + 2x + 3x = 18x2 + -3x + -3

Combine like terms: -1 + 1 = 0
0 + 2x + 3x = 18x2 + -3x + -3
2x + 3x = 18x2 + -3x + -3

Combine like terms: 2x + 3x = 5x
5x = 18x2 + -3x + -3

Reorder the terms:
5x = -3 + -3x + 18x2

Solving
5x = -3 + -3x + 18x2

Solving for variable 'x'.

Reorder the terms:
3 + 5x + 3x + -18x2 = -3 + -3x + 18x2 + 3 + 3x + -18x2

Combine like terms: 5x + 3x = 8x
3 + 8x + -18x2 = -3 + -3x + 18x2 + 3 + 3x + -18x2

Reorder the terms:
3 + 8x + -18x2 = -3 + 3 + -3x + 3x + 18x2 + -18x2

Combine like terms: -3 + 3 = 0
3 + 8x + -18x2 = 0 + -3x + 3x + 18x2 + -18x2
3 + 8x + -18x2 = -3x + 3x + 18x2 + -18x2

Combine like terms: -3x + 3x = 0
3 + 8x + -18x2 = 0 + 18x2 + -18x2
3 + 8x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
3 + 8x + -18x2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
-0.1666666667 + -0.4444444444x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -0.4444444444x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -0.4444444444x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -0.4444444444x + x2 = 0 + 0.1666666667
-0.4444444444x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-0.4444444444x + x2 = 0.1666666667

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 = 0.1666666667 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444x + x2 = 0.1666666667 + 0.04938271604

Combine like terms: 0.1666666667 + 0.04938271604 = 0.21604938274
0.04938271604 + -0.4444444444x + x2 = 0.21604938274

Factor a perfect square on the left side:
(x + -0.2222222222)(x + -0.2222222222) = 0.21604938274

Calculate the square root of the right side: 0.464811126

Break this problem into two subproblems by setting 
(x + -0.2222222222) equal to 0.464811126 and -0.464811126.

Subproblem 1
x + -0.2222222222 = 0.464811126

Simplifying
x + -0.2222222222 = 0.464811126

Reorder the terms:
-0.2222222222 + x = 0.464811126

Solving
-0.2222222222 + x = 0.464811126

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 = 0.464811126 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x = 0.464811126 + 0.2222222222
x = 0.464811126 + 0.2222222222

Combine like terms: 0.464811126 + 0.2222222222 = 0.6870333482
x = 0.6870333482

Simplifying
x = 0.6870333482

Subproblem 2
x + -0.2222222222 = -0.464811126

Simplifying
x + -0.2222222222 = -0.464811126

Reorder the terms:
-0.2222222222 + x = -0.464811126

Solving
-0.2222222222 + x = -0.464811126

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 = -0.464811126 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + x = -0.464811126 + 0.2222222222
x = -0.464811126 + 0.2222222222

Combine like terms: -0.464811126 + 0.2222222222 = -0.2425889038
x = -0.2425889038

Simplifying
x = -0.2425889038

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6870333482, -0.2425889038}