2x(1+3x)-1+3=0

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Solution for 2x(1+3x)-1+3=0 equation: 


Simplifying
2x(1 + 3x) + -1 + 3 = 0
(1 * 2x + 3x * 2x) + -1 + 3 = 0
(2x + 6x2) + -1 + 3 = 0

Reorder the terms:
-1 + 3 + 2x + 6x2 = 0

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

Solving
2 + 2x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + x + 3x2) = 0

Ignore the factor 2.

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

Simplifying
1 + x + 3x2 = 0

Solving
1 + x + 3x2 = 0

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

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

Move the constant term to the right:

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

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

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

Combine like terms: 0 + -0.3333333333 = -0.3333333333
0.3333333333x + 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.
0.3333333333x + 0.25 + x2 = -0.3333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = -0.3333333333 + 0.25

Combine like terms: -0.3333333333 + 0.25 = -0.0833333333
0.25 + 0.3333333333x + 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.

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