18v^2+24v+12=0

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Solution for 18v^2+24v+12=0 equation: 


Simplifying
18v2 + 24v + 12 = 0

Reorder the terms:
12 + 24v + 18v2 = 0

Solving
12 + 24v + 18v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + 4v + 3v2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(2 + 4v + 3v2)' equal to zero and attempt to solve:

Simplifying
2 + 4v + 3v2 = 0

Solving
2 + 4v + 3v2 = 0

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

Divide each side by '3'.
0.6666666667 + 1.333333333v + v2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 1.333333333v + -0.6666666667 + v2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 1.333333333v + v2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 1.333333333v + v2 = 0 + -0.6666666667
1.333333333v + v2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
1.333333333v + v2 = -0.6666666667

The v term is 1.333333333v.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333v + 0.4444444442 + v2 = -0.6666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333v + v2 = -0.6666666667 + 0.4444444442

Combine like terms: -0.6666666667 + 0.4444444442 = -0.2222222225
0.4444444442 + 1.333333333v + v2 = -0.2222222225

Factor a perfect square on the left side:
(v + 0.6666666665)(v + 0.6666666665) = -0.2222222225

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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