12ad^3=15a^3d

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Solution for 12ad^3=15a^3d equation: 


Simplifying
12ad3 = 15a3d

Solving
12ad3 = 15a3d

Solving for variable 'a'.

Combine like terms: 15a3d + -15a3d = 0
12ad3 + -15a3d = 0

Factor out the Greatest Common Factor (GCF), '3ad'.
3ad(4d2 + -5a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'ad' equal to zero and attempt to solve:

Simplifying
ad = 0

Solving
ad = 0

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

Simplifying
ad = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(4d2 + -5a2)' equal to zero and attempt to solve:

Simplifying
4d2 + -5a2 = 0

Reorder the terms:
-5a2 + 4d2 = 0

Solving
-5a2 + 4d2 = 0

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

Add '-4d2' to each side of the equation.
-5a2 + 4d2 + -4d2 = 0 + -4d2

Combine like terms: 4d2 + -4d2 = 0
-5a2 + 0 = 0 + -4d2
-5a2 = 0 + -4d2
Remove the zero:
-5a2 = -4d2

Divide each side by '-5'.
a2 = 0.8d2

Simplifying
a2 = 0.8d2

Take the square root of each side:
a = {-0.894427191d, 0.894427191d}
Solution
a = {-0.894427191d, 0.894427191d}

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