x(3x+1)=-6

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Solution for x(3x+1)=-6 equation:


Simplifying
x(3x + 1) = -6

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

Solving
1x + 3x2 = -6

Solving for variable 'x'.

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

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

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

Divide each side by '3'.
2 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.3333333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 0.3333333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.3333333333x + x2 = 0 + -2
0.3333333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.3333333333x + x2 = -2

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = -2 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = -2 + 0.02777777779

Combine like terms: -2 + 0.02777777779 = -1.97222222221
0.02777777779 + 0.3333333333x + x2 = -1.97222222221

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = -1.97222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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