(5a^3+6a)+(-3a^2-5a)=

Solution for (5a^3+6a)+(-3a^2-5a)= equation:

Simplifying
(5a3 + 6a) + (-3a2 + -5a) = 0

Reorder the terms:
(6a + 5a3) + (-3a2 + -5a) = 0

Remove parenthesis around (6a + 5a3)
6a + 5a3 + (-3a2 + -5a) = 0

Reorder the terms:
6a + 5a3 + (-5a + -3a2) = 0

Remove parenthesis around (-5a + -3a2)
6a + 5a3 + -5a + -3a2 = 0

Reorder the terms:
6a + -5a + -3a2 + 5a3 = 0

Combine like terms: 6a + -5a = 1a
1a + -3a2 + 5a3 = 0

Solving
1a + -3a2 + 5a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(1 + -3a + 5a2) = 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 '(1 + -3a + 5a2)' equal to zero and attempt to solve:

Simplifying
1 + -3a + 5a2 = 0

Solving
1 + -3a + 5a2 = 0

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

Divide each side by '5'.
0.2 + -0.6a + a2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -0.6a + -0.2 + a2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -0.6a + a2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -0.6a + a2 = 0 + -0.2
-0.6a + a2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-0.6a + a2 = -0.2

The a term is -0.6a.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6a + 0.09 + a2 = -0.2 + 0.09

Reorder the terms:
0.09 + -0.6a + a2 = -0.2 + 0.09

Combine like terms: -0.2 + 0.09 = -0.11
0.09 + -0.6a + a2 = -0.11

Factor a perfect square on the left side:
(a + -0.3)(a + -0.3) = -0.11

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}