3x(x+1)=x-2

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


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

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

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

Solving
3x + 3x2 = -2 + x

Solving for variable 'x'.

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

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

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

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

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

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

Divide each side by '3'.
0.6666666667 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 0.6666666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 0.6666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 0.6666666667x + x2 = 0 + -0.6666666667
0.6666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
0.6666666667x + x2 = -0.6666666667

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = -0.6666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = -0.6666666667 + 0.1111111112

Combine like terms: -0.6666666667 + 0.1111111112 = -0.5555555555
0.1111111112 + 0.6666666667x + x2 = -0.5555555555

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = -0.5555555555

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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