4a^3-16a^2=180a

Solution for 4a^3-16a^2=180a equation:

Simplifying
4a3 + -16a2 = 180a

Reorder the terms:
-16a2 + 4a3 = 180a

Solving
-16a2 + 4a3 = 180a

Solving for variable 'a'.

Reorder the terms:
-180a + -16a2 + 4a3 = 180a + -180a

Combine like terms: 180a + -180a = 0
-180a + -16a2 + 4a3 = 0

Factor out the Greatest Common Factor (GCF), '4a'.
4a(-45 + -4a + a2) = 0

Factor a trinomial.
4a((-5 + -1a)(9 + -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 '(-5 + -1a)' equal to zero and attempt to solve:

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 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 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

Simplifying
a = -5
Subproblem 3
Set the factor '(9 + -1a)' equal to zero and attempt to solve:

Simplifying
9 + -1a = 0

Solving
9 + -1a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1a = 0 + -9
-1a = 0 + -9

Combine like terms: 0 + -9 = -9
-1a = -9

Divide each side by '-1'.
a = 9

Simplifying
a = 9
Solution
a = {0, -5, 9}