5a^2x^2=10a^3y^3

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Solution for 5a^2x^2=10a^3y^3 equation: 


Simplifying
5a2x2 = 10a3y3

Solving
5a2x2 = 10a3y3

Solving for variable 'a'.

Combine like terms: 10a3y3 + -10a3y3 = 0
5a2x2 + -10a3y3 = 0

Factor out the Greatest Common Factor (GCF), '5a2'.
5a2(x2 + -2ay3) = 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 '(x2 + -2ay3)' equal to zero and attempt to solve:

Simplifying
x2 + -2ay3 = 0

Reorder the terms:
-2ay3 + x2 = 0

Solving
-2ay3 + x2 = 0

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

Add '-1x2' to each side of the equation.
-2ay3 + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
-2ay3 + 0 = 0 + -1x2
-2ay3 = 0 + -1x2
Remove the zero:
-2ay3 = -1x2

Divide each side by '-2y3'.
a = 0.5x2y-3

Simplifying
a = 0.5x2y-3
Solution
a = {0, 0.5x2y-3}

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