10a^3+9a^2+2a=

Solution for 10a^3+9a^2+2a= equation:

Simplifying
10a3 + 9a2 + 2a = 0

Reorder the terms:
2a + 9a2 + 10a3 = 0

Solving
2a + 9a2 + 10a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(2 + 9a + 10a2) = 0

Factor a trinomial.
a((1 + 2a)(2 + 5a)) = 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 '(1 + 2a)' equal to zero and attempt to solve:

Simplifying
1 + 2a = 0

Solving
1 + 2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 3
Set the factor '(2 + 5a)' equal to zero and attempt to solve:

Simplifying
2 + 5a = 0

Solving
2 + 5a = 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 + 5a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5a = 0 + -2
5a = 0 + -2

Combine like terms: 0 + -2 = -2
5a = -2

Divide each side by '5'.
a = -0.4

Simplifying
a = -0.4
Solution
a = {0, -0.5, -0.4}