a^5-13a^4+42a^3=

Solution for a^5-13a^4+42a^3= equation:

Simplifying
a5 + -13a4 + 42a3 = 0

Reorder the terms:
42a3 + -13a4 + a5 = 0

Solving
42a3 + -13a4 + a5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a3'.
a3(42 + -13a + a2) = 0

Factor a trinomial.
a3((6 + -1a)(7 + -1a)) = 0

Subproblem 1
Set the factor 'a3' equal to zero and attempt to solve:

Simplifying
a3 = 0

Solving
a3 = 0

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

Simplifying
a3 = 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 '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Subproblem 3
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {6, 7}