a^8-4a^7+4a^6=

Solution for a^8-4a^7+4a^6= equation:

Simplifying
a8 + -4a7 + 4a6 = 0

Reorder the terms:
4a6 + -4a7 + a8 = 0

Solving
4a6 + -4a7 + a8 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a6'.
a6(4 + -4a + a2) = 0

Factor a trinomial.
a6((2 + -1a)(2 + -1a)) = 0

Subproblem 1
Set the factor 'a6' equal to zero and attempt to solve:

Simplifying
a6 = 0

Solving
a6 = 0

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

Simplifying
a6 = 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 '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

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

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

Divide each side by '-1'.
a = 2

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {2, 2}