(-4a^4-7a^3)+(-7a^4-4a^2)=

Solution for (-4a^4-7a^3)+(-7a^4-4a^2)= equation:

Simplifying
(-4a4 + -7a3) + (-7a4 + -4a2) = 0

Reorder the terms:
(-7a3 + -4a4) + (-7a4 + -4a2) = 0

Remove parenthesis around (-7a3 + -4a4)
-7a3 + -4a4 + (-7a4 + -4a2) = 0

Reorder the terms:
-7a3 + -4a4 + (-4a2 + -7a4) = 0

Remove parenthesis around (-4a2 + -7a4)
-7a3 + -4a4 + -4a2 + -7a4 = 0

Reorder the terms:
-4a2 + -7a3 + -4a4 + -7a4 = 0

Combine like terms: -4a4 + -7a4 = -11a4
-4a2 + -7a3 + -11a4 = 0

Solving
-4a2 + -7a3 + -11a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-1a2'.
-1a2(4 + 7a + 11a2) = 0

Ignore the factor -1.
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 '(4 + 7a + 11a2)' equal to zero and attempt to solve:

Simplifying
4 + 7a + 11a2 = 0

Solving
4 + 7a + 11a2 = 0

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

Divide each side by '11'.
0.3636363636 + 0.6363636364a + a2 = 0

Move the constant term to the right:

Add '-0.3636363636' to each side of the equation.
0.3636363636 + 0.6363636364a + -0.3636363636 + a2 = 0 + -0.3636363636

Reorder the terms:
0.3636363636 + -0.3636363636 + 0.6363636364a + a2 = 0 + -0.3636363636

Combine like terms: 0.3636363636 + -0.3636363636 = 0.0000000000
0.0000000000 + 0.6363636364a + a2 = 0 + -0.3636363636
0.6363636364a + a2 = 0 + -0.3636363636

Combine like terms: 0 + -0.3636363636 = -0.3636363636
0.6363636364a + a2 = -0.3636363636

The a term is 0.6363636364a.  Take half its coefficient (0.3181818182).
Square it (0.1012396694) and add it to both sides.

Add '0.1012396694' to each side of the equation.
0.6363636364a + 0.1012396694 + a2 = -0.3636363636 + 0.1012396694

Reorder the terms:
0.1012396694 + 0.6363636364a + a2 = -0.3636363636 + 0.1012396694

Combine like terms: -0.3636363636 + 0.1012396694 = -0.2623966942
0.1012396694 + 0.6363636364a + a2 = -0.2623966942

Factor a perfect square on the left side:
(a + 0.3181818182)(a + 0.3181818182) = -0.2623966942

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}