10a^3-5a^2=0

Solution for 10a^3-5a^2=0 equation:

Simplifying
10a3 + -5a2 = 0

Reorder the terms:
-5a2 + 10a3 = 0

Solving
-5a2 + 10a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5a2'.
5a2(-1 + 2a) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
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
Solution
a = {0, 0.5}