(4a^3)-(48a^2)+(80a)=0

Solution for (4a^3)-(48a^2)+(80a)=0 equation:

Simplifying
(4a3) + -1(48a2) + (80a) = 0

Remove parenthesis around (48a2)
(4a3) + -1 * 48a2 + (80a) = 0

Multiply -1 * 48
(4a3) + -48a2 + (80a) = 0

Reorder the terms:
(80a) + -48a2 + (4a3) = 0

Solving
(80a) + -48a2 + (4a3) = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(20 + -12a + a2) = 0

Factor a trinomial.
4a((2 + -1a)(10 + -1a)) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
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 '(10 + -1a)' equal to zero and attempt to solve:

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1a = 0 + -10
-1a = 0 + -10

Combine like terms: 0 + -10 = -10
-1a = -10

Divide each side by '-1'.
a = 10

Simplifying
a = 10
Solution
a = {0, 2, 10}