a^3+3a^2=10a

Solution for a^3+3a^2=10a equation:

Simplifying
a3 + 3a2 = 10a

Reorder the terms:
3a2 + a3 = 10a

Solving
3a2 + a3 = 10a

Solving for variable 'a'.

Reorder the terms:
-10a + 3a2 + a3 = 10a + -10a

Combine like terms: 10a + -10a = 0
-10a + 3a2 + a3 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-10 + 3a + a2) = 0

Factor a trinomial.
a((-5 + -1a)(2 + -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 '(-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 '(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 = {0, -5, 2}