6a^3+13a^2+15a=

Solution for 6a^3+13a^2+15a= equation:

Simplifying
6a3 + 13a2 + 15a = 0

Reorder the terms:
15a + 13a2 + 6a3 = 0

Solving
15a + 13a2 + 6a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(15 + 13a + 6a2) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0
Subproblem 2
Set the factor '(15 + 13a + 6a2)' equal to zero and attempt to solve:

Simplifying
15 + 13a + 6a2 = 0

Solving
15 + 13a + 6a2 = 0

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

Divide each side by '6'.
2.5 + 2.166666667a + a2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 2.166666667a + -2.5 + a2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 2.166666667a + a2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 2.166666667a + a2 = 0 + -2.5
2.166666667a + a2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
2.166666667a + a2 = -2.5

The a term is 2.166666667a.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667a + 1.173611113 + a2 = -2.5 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667a + a2 = -2.5 + 1.173611113

Combine like terms: -2.5 + 1.173611113 = -1.326388887
1.173611113 + 2.166666667a + a2 = -1.326388887

Factor a perfect square on the left side:
(a + 1.083333334)(a + 1.083333334) = -1.326388887

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.
Solution
a = {0}