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

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

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

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

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

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

Multiply (-1 + 3x) * (2 + x)
1 + -2(-1(2 + x) + 3x * (2 + x)) + 3x = -1
1 + -2((2 * -1 + x * -1) + 3x * (2 + x)) + 3x = -1
1 + -2((-2 + -1x) + 3x * (2 + x)) + 3x = -1
1 + -2(-2 + -1x + (2 * 3x + x * 3x)) + 3x = -1
1 + -2(-2 + -1x + (6x + 3x2)) + 3x = -1

Combine like terms: -1x + 6x = 5x
1 + -2(-2 + 5x + 3x2) + 3x = -1
1 + (-2 * -2 + 5x * -2 + 3x2 * -2) + 3x = -1
1 + (4 + -10x + -6x2) + 3x = -1

Reorder the terms:
1 + 4 + -10x + 3x + -6x2 = -1

Combine like terms: 1 + 4 = 5
5 + -10x + 3x + -6x2 = -1

Combine like terms: -10x + 3x = -7x
5 + -7x + -6x2 = -1

Solving
5 + -7x + -6x2 = -1

Solving for variable 'x'.

Reorder the terms:
5 + 1 + -7x + -6x2 = -1 + 1

Combine like terms: 5 + 1 = 6
6 + -7x + -6x2 = -1 + 1

Combine like terms: -1 + 1 = 0
6 + -7x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1 + 1.166666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.166666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.166666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.166666667x + x2 = 0 + 1
1.166666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.166666667x + x2 = 1

The x term is 1.166666667x.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667x + 0.3402777780 + x2 = 1 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667x + x2 = 1 + 0.3402777780

Combine like terms: 1 + 0.3402777780 = 1.340277778
0.3402777780 + 1.166666667x + x2 = 1.340277778

Factor a perfect square on the left side:
(x + 0.5833333335)(x + 0.5833333335) = 1.340277778

Calculate the square root of the right side: 1.157703666

Break this problem into two subproblems by setting 
(x + 0.5833333335) equal to 1.157703666 and -1.157703666.

Subproblem 1
x + 0.5833333335 = 1.157703666

Simplifying
x + 0.5833333335 = 1.157703666

Reorder the terms:
0.5833333335 + x = 1.157703666

Solving
0.5833333335 + x = 1.157703666

Solving for variable 'x'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + x = 1.157703666 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + x = 1.157703666 + -0.5833333335
x = 1.157703666 + -0.5833333335

Combine like terms: 1.157703666 + -0.5833333335 = 0.5743703325
x = 0.5743703325

Simplifying
x = 0.5743703325

Subproblem 2
x + 0.5833333335 = -1.157703666

Simplifying
x + 0.5833333335 = -1.157703666

Reorder the terms:
0.5833333335 + x = -1.157703666

Solving
0.5833333335 + x = -1.157703666

Solving for variable 'x'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + x = -1.157703666 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + x = -1.157703666 + -0.5833333335
x = -1.157703666 + -0.5833333335

Combine like terms: -1.157703666 + -0.5833333335 = -1.7410369995
x = -1.7410369995

Simplifying
x = -1.7410369995

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5743703325, -1.7410369995}