4a^7-8a^6-12a^5=0

Solution for 4a^7-8a^6-12a^5=0 equation:

Simplifying
4a7 + -8a6 + -12a5 = 0

Reorder the terms:
-12a5 + -8a6 + 4a7 = 0

Solving
-12a5 + -8a6 + 4a7 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a5'.
4a5(-3 + -2a + a2) = 0

Factor a trinomial.
4a5((-1 + -1a)(3 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a5' equal to zero and attempt to solve:

Simplifying
a5 = 0

Solving
a5 = 0

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

Simplifying
a5 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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 '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-1, 3}