18x^2+27x+12=0

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Solution for 18x^2+27x+12=0 equation: 


Simplifying
18x2 + 27x + 12 = 0

Reorder the terms:
12 + 27x + 18x2 = 0

Solving
12 + 27x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 9x + 6x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + 9x + 6x2)' equal to zero and attempt to solve:

Simplifying
4 + 9x + 6x2 = 0

Solving
4 + 9x + 6x2 = 0

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

Divide each side by '6'.
0.6666666667 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 1.5x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 1.5x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 1.5x + x2 = 0 + -0.6666666667
1.5x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
1.5x + x2 = -0.6666666667

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -0.6666666667 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -0.6666666667 + 0.5625

Combine like terms: -0.6666666667 + 0.5625 = -0.1041666667
0.5625 + 1.5x + x2 = -0.1041666667

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -0.1041666667

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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