5a^2c^3(3a+5cd^2-2d)=0

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Solution for 5a^2c^3(3a+5cd^2-2d)=0 equation: 


Simplifying
5a2c3(3a + 5cd2 + -2d) = 0
(3a * 5a2c3 + 5cd2 * 5a2c3 + -2d * 5a2c3) = 0

Reorder the terms:
(-10a2c3d + 25a2c4d2 + 15a3c3) = 0
(-10a2c3d + 25a2c4d2 + 15a3c3) = 0

Solving
-10a2c3d + 25a2c4d2 + 15a3c3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5a2c3'.
5a2c3(-2d + 5cd2 + 3a) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'a2c3' equal to zero and attempt to solve:

Simplifying
a2c3 = 0

Solving
a2c3 = 0

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

Simplifying
a2c3 = 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 '(-2d + 5cd2 + 3a)' equal to zero and attempt to solve:

Simplifying
-2d + 5cd2 + 3a = 0

Reorder the terms:
3a + 5cd2 + -2d = 0

Solving
3a + 5cd2 + -2d = 0

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

Add '-5cd2' to each side of the equation.
3a + 5cd2 + -5cd2 + -2d = 0 + -5cd2

Combine like terms: 5cd2 + -5cd2 = 0
3a + 0 + -2d = 0 + -5cd2
3a + -2d = 0 + -5cd2
Remove the zero:
3a + -2d = -5cd2

Add '2d' to each side of the equation.
3a + -2d + 2d = -5cd2 + 2d

Combine like terms: -2d + 2d = 0
3a + 0 = -5cd2 + 2d
3a = -5cd2 + 2d

Divide each side by '3'.
a = -1.666666667cd2 + 0.6666666667d

Simplifying
a = -1.666666667cd2 + 0.6666666667d
Solution
a = {-1.666666667cd2 + 0.6666666667d}

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