12x^2+9x+15=0

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Solution for 12x^2+9x+15=0 equation: 


Simplifying
12x2 + 9x + 15 = 0

Reorder the terms:
15 + 9x + 12x2 = 0

Solving
15 + 9x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 3x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + 3x + 4x2)' equal to zero and attempt to solve:

Simplifying
5 + 3x + 4x2 = 0

Solving
5 + 3x + 4x2 = 0

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

Divide each side by '4'.
1.25 + 0.75x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 0.75x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 0.75x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 0.75x + x2 = 0 + -1.25
0.75x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
0.75x + x2 = -1.25

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = -1.25 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = -1.25 + 0.140625

Combine like terms: -1.25 + 0.140625 = -1.109375
0.140625 + 0.75x + x2 = -1.109375

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = -1.109375

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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