6a^4+13a^3+5a^2=0

Solution for 6a^4+13a^3+5a^2=0 equation:

Simplifying
6a4 + 13a3 + 5a2 = 0

Reorder the terms:
5a2 + 13a3 + 6a4 = 0

Solving
5a2 + 13a3 + 6a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(5 + 13a + 6a2) = 0

Factor a trinomial.
a2((5 + 3a)(1 + 2a)) = 0

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(5 + 3a)' equal to zero and attempt to solve:

Simplifying
5 + 3a = 0

Solving
5 + 3a = 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 + 3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3a = 0 + -5
3a = 0 + -5

Combine like terms: 0 + -5 = -5
3a = -5

Divide each side by '3'.
a = -1.666666667

Simplifying
a = -1.666666667
Subproblem 3
Set the factor '(1 + 2a)' equal to zero and attempt to solve:

Simplifying
1 + 2a = 0

Solving
1 + 2a = 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 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {0, -1.666666667, -0.5}