3a^2=5a^3

Solution for 3a^2=5a^3 equation:

Simplifying
3a2 = 5a3

Solving
3a2 = 5a3

Solving for variable 'a'.

Combine like terms: 5a3 + -5a3 = 0
3a2 + -5a3 = 0

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(3 + -5a) = 0

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 '(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
Solution
a = {0, 0.6}