10a^3+a^2=3a

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

Simplifying
10a3 + a2 = 3a

Reorder the terms:
a2 + 10a3 = 3a

Solving
a2 + 10a3 = 3a

Solving for variable 'a'.

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

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

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

Factor a trinomial.
a((-3 + -5a)(1 + -2a)) = 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 '(-3 + -5a)' equal to zero and attempt to solve:

Simplifying
-3 + -5a = 0

Solving
-3 + -5a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5a = 0 + 3
-5a = 0 + 3

Combine like terms: 0 + 3 = 3
-5a = 3

Divide each side by '-5'.
a = -0.6

Simplifying
a = -0.6
Subproblem 3
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
Solution
a = {0, -0.6, 0.5}