a^3-20a^2=-100a

Solution for a^3-20a^2=-100a equation:

Simplifying
a3 + -20a2 = -100a

Reorder the terms:
-20a2 + a3 = -100a

Solving
-20a2 + a3 = -100a

Solving for variable 'a'.

Reorder the terms:
100a + -20a2 + a3 = -100a + 100a

Combine like terms: -100a + 100a = 0
100a + -20a2 + a3 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(100 + -20a + a2) = 0

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

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 '(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
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, 10, 10}