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

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

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

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

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

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

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

Combine like terms: 6x + 2x = 8x
-2 + 8x + 3x2 = x + 1

Reorder the terms:
-2 + 8x + 3x2 = 1 + x

Solving
-2 + 8x + 3x2 = 1 + x

Solving for variable 'x'.

Reorder the terms:
-2 + -1 + 8x + -1x + 3x2 = 1 + x + -1 + -1x

Combine like terms: -2 + -1 = -3
-3 + 8x + -1x + 3x2 = 1 + x + -1 + -1x

Combine like terms: 8x + -1x = 7x
-3 + 7x + 3x2 = 1 + x + -1 + -1x

Reorder the terms:
-3 + 7x + 3x2 = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
-3 + 7x + 3x2 = 0 + x + -1x
-3 + 7x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-3 + 7x + 3x2 = 0

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

Divide each side by '3'.
-1 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.333333333x + x2 = 0 + 1
2.333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.333333333x + x2 = 1

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 1 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 1 + 1.361111112

Combine like terms: 1 + 1.361111112 = 2.361111112
1.361111112 + 2.333333333x + x2 = 2.361111112

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 2.361111112

Calculate the square root of the right side: 1.536590743

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 1.536590743 and -1.536590743.

Subproblem 1
x + 1.166666667 = 1.536590743

Simplifying
x + 1.166666667 = 1.536590743

Reorder the terms:
1.166666667 + x = 1.536590743

Solving
1.166666667 + x = 1.536590743

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 1.536590743 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 1.536590743 + -1.166666667
x = 1.536590743 + -1.166666667

Combine like terms: 1.536590743 + -1.166666667 = 0.369924076
x = 0.369924076

Simplifying
x = 0.369924076

Subproblem 2
x + 1.166666667 = -1.536590743

Simplifying
x + 1.166666667 = -1.536590743

Reorder the terms:
1.166666667 + x = -1.536590743

Solving
1.166666667 + x = -1.536590743

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -1.536590743 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -1.536590743 + -1.166666667
x = -1.536590743 + -1.166666667

Combine like terms: -1.536590743 + -1.166666667 = -2.70325741
x = -2.70325741

Simplifying
x = -2.70325741

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.369924076, -2.70325741}