12a^2+6a^3-3a^3-2a^2-5a^2-8a^4=

Solution for 12a^2+6a^3-3a^3-2a^2-5a^2-8a^4= equation:

Simplifying
12a2 + 6a3 + -3a3 + -2a2 + -5a2 + -8a4 = 0

Reorder the terms:
12a2 + -2a2 + -5a2 + 6a3 + -3a3 + -8a4 = 0

Combine like terms: 12a2 + -2a2 = 10a2
10a2 + -5a2 + 6a3 + -3a3 + -8a4 = 0

Combine like terms: 10a2 + -5a2 = 5a2
5a2 + 6a3 + -3a3 + -8a4 = 0

Combine like terms: 6a3 + -3a3 = 3a3
5a2 + 3a3 + -8a4 = 0

Solving
5a2 + 3a3 + -8a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(5 + 3a + -8a2) = 0

Factor a trinomial.
a2((1 + -1a)(5 + 8a)) = 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 '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Subproblem 3
Set the factor '(5 + 8a)' equal to zero and attempt to solve:

Simplifying
5 + 8a = 0

Solving
5 + 8a = 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 + 8a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8a = 0 + -5
8a = 0 + -5

Combine like terms: 0 + -5 = -5
8a = -5

Divide each side by '8'.
a = -0.625

Simplifying
a = -0.625
Solution
a = {0, 1, -0.625}