15a^2+123a+354=0

Solution for 15a^2+123a+354=0 equation:

Simplifying
15a2 + 123a + 354 = 0

Reorder the terms:
354 + 123a + 15a2 = 0

Solving
354 + 123a + 15a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(118 + 41a + 5a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(118 + 41a + 5a2)' equal to zero and attempt to solve:

Simplifying
118 + 41a + 5a2 = 0

Solving
118 + 41a + 5a2 = 0

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

Divide each side by '5'.
23.6 + 8.2a + a2 = 0

Move the constant term to the right:

Add '-23.6' to each side of the equation.
23.6 + 8.2a + -23.6 + a2 = 0 + -23.6

Reorder the terms:
23.6 + -23.6 + 8.2a + a2 = 0 + -23.6

Combine like terms: 23.6 + -23.6 = 0.0
0.0 + 8.2a + a2 = 0 + -23.6
8.2a + a2 = 0 + -23.6

Combine like terms: 0 + -23.6 = -23.6
8.2a + a2 = -23.6

The a term is 8.2a.  Take half its coefficient (4.1).
Square it (16.81) and add it to both sides.

Add '16.81' to each side of the equation.
8.2a + 16.81 + a2 = -23.6 + 16.81

Reorder the terms:
16.81 + 8.2a + a2 = -23.6 + 16.81

Combine like terms: -23.6 + 16.81 = -6.79
16.81 + 8.2a + a2 = -6.79

Factor a perfect square on the left side:
(a + 4.1)(a + 4.1) = -6.79

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.