(3a^3-a^2b)(5ab-2b^2)=0

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Solution for (3a^3-a^2b)(5ab-2b^2)=0 equation: 


Simplifying
(3a3 + -1a2b)(5ab + -2b2) = 0

Reorder the terms:
(-1a2b + 3a3)(5ab + -2b2) = 0

Multiply (-1a2b + 3a3) * (5ab + -2b2)
(-1a2b * (5ab + -2b2) + 3a3 * (5ab + -2b2)) = 0
((5ab * -1a2b + -2b2 * -1a2b) + 3a3 * (5ab + -2b2)) = 0

Reorder the terms:
((2a2b3 + -5a3b2) + 3a3 * (5ab + -2b2)) = 0
((2a2b3 + -5a3b2) + 3a3 * (5ab + -2b2)) = 0
(2a2b3 + -5a3b2 + (5ab * 3a3 + -2b2 * 3a3)) = 0

Reorder the terms:
(2a2b3 + -5a3b2 + (-6a3b2 + 15a4b)) = 0
(2a2b3 + -5a3b2 + (-6a3b2 + 15a4b)) = 0

Combine like terms: -5a3b2 + -6a3b2 = -11a3b2
(2a2b3 + -11a3b2 + 15a4b) = 0

Solving
2a2b3 + -11a3b2 + 15a4b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2b'.
a2b(2b2 + -11ab + 15a2) = 0

Factor a trinomial.
a2b((b + -3a)(2b + -5a)) = 0


Subproblem 1
Set the factor 'a2b' equal to zero and attempt to solve:

Simplifying
a2b = 0

Solving
a2b = 0

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

Simplifying
a2b = 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 '(b + -3a)' equal to zero and attempt to solve:

Simplifying
b + -3a = 0

Reorder the terms:
-3a + b = 0

Solving
-3a + b = 0

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

Add '-1b' to each side of the equation.
-3a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-3a + 0 = 0 + -1b
-3a = 0 + -1b
Remove the zero:
-3a = -1b

Divide each side by '-3'.
a = 0.3333333333b

Simplifying
a = 0.3333333333b

Subproblem 3
Set the factor '(2b + -5a)' equal to zero and attempt to solve:

Simplifying
2b + -5a = 0

Reorder the terms:
-5a + 2b = 0

Solving
-5a + 2b = 0

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

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

Combine like terms: 2b + -2b = 0
-5a + 0 = 0 + -2b
-5a = 0 + -2b
Remove the zero:
-5a = -2b

Divide each side by '-5'.
a = 0.4b

Simplifying
a = 0.4b
Solution
a = {0.3333333333b, 0.4b}

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