6a^3+17a^2+5a=0

Solution for 6a^3+17a^2+5a=0 equation:

Simplifying
6a3 + 17a2 + 5a = 0

Reorder the terms:
5a + 17a2 + 6a3 = 0

Solving
5a + 17a2 + 6a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(5 + 17a + 6a2) = 0

Factor a trinomial.
a((5 + 2a)(1 + 3a)) = 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 '(5 + 2a)' equal to zero and attempt to solve:

Simplifying
5 + 2a = 0

Solving
5 + 2a = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2a = 0 + -5
2a = 0 + -5

Combine like terms: 0 + -5 = -5
2a = -5

Divide each side by '2'.
a = -2.5

Simplifying
a = -2.5
Subproblem 3
Set the factor '(1 + 3a)' equal to zero and attempt to solve:

Simplifying
1 + 3a = 0

Solving
1 + 3a = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3a = 0 + -1
3a = 0 + -1

Combine like terms: 0 + -1 = -1
3a = -1

Divide each side by '3'.
a = -0.3333333333

Simplifying
a = -0.3333333333
Solution
a = {0, -2.5, -0.3333333333}