(x+1)[2x+1]=x

Solution for (x+1)[2x+1]=x equation:

Simplifying
(x + 1)[2x + 1] = x

Reorder the terms:
(1 + x)[2x + 1] = x

Reorder the terms:
(1 + x)[1 + 2x] = x

Multiply (1 + x) * [1 + 2x]
(1[1 + 2x] + x[1 + 2x]) = x
([1 * 1 + 2x * 1] + x[1 + 2x]) = x
([1 + 2x] + x[1 + 2x]) = x
(1 + 2x + [1 * x + 2x * x]) = x
(1 + 2x + [1x + 2x2]) = x

Combine like terms: 2x + 1x = 3x
(1 + 3x + 2x2) = x

Solving
1 + 3x + 2x2 = x

Solving for variable 'x'.

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

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

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

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

Divide each side by '2'.
0.5 + x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x + x2 = 0 + -0.5
x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
x + x2 = -0.5

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 = -0.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
1.25 + x2 = -0.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.