3(2x+1)x=-39

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Solution for 3(2x+1)x=-39 equation: 


Simplifying
3(2x + 1) * x = -39

Reorder the terms:
3(1 + 2x) * x = -39

Reorder the terms for easier multiplication:
3x(1 + 2x) = -39
(1 * 3x + 2x * 3x) = -39
(3x + 6x2) = -39

Solving
3x + 6x2 = -39

Solving for variable 'x'.

Reorder the terms:
39 + 3x + 6x2 = -39 + 39

Combine like terms: -39 + 39 = 0
39 + 3x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(13 + x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(13 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
13 + x + 2x2 = 0

Solving
13 + x + 2x2 = 0

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

Divide each side by '2'.
6.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + 0.5x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + 0.5x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + 0.5x + x2 = 0 + -6.5
0.5x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
0.5x + x2 = -6.5

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.
0.5x + 0.25 + x2 = -6.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = -6.5 + 0.25

Combine like terms: -6.5 + 0.25 = -6.25
0.25 + 0.5x + x2 = -6.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -6.25

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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