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

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

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

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

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

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

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

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

Reorder the terms for easier multiplication:
1 + 3x = 3x(2 + x) + 2
1 + 3x = (2 * 3x + x * 3x) + 2
1 + 3x = (6x + 3x2) + 2

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

Solving
1 + 3x = 2 + 6x + 3x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 3x + 3x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 3x + 3x2)' equal to zero and attempt to solve:

Simplifying
1 + 3x + 3x2 = 0

Solving
1 + 3x + 3x2 = 0

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

Divide each side by '3'.
0.3333333333 + x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + x + x2 = 0 + -0.3333333333
x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
x + x2 = -0.3333333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = -0.3333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -0.3333333333 + 0.25

Combine like terms: -0.3333333333 + 0.25 = -0.0833333333
1.25 + x2 = -0.0833333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.0833333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.