(5a^2-10ab^3)(2a^2-5ab^3)=

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Solution for (5a^2-10ab^3)(2a^2-5ab^3)= equation: 


Simplifying
(5a2 + -10ab3)(2a2 + -5ab3) = 0

Reorder the terms:
(-10ab3 + 5a2)(2a2 + -5ab3) = 0

Reorder the terms:
(-10ab3 + 5a2)(-5ab3 + 2a2) = 0

Multiply (-10ab3 + 5a2) * (-5ab3 + 2a2)
(-10ab3 * (-5ab3 + 2a2) + 5a2 * (-5ab3 + 2a2)) = 0
((-5ab3 * -10ab3 + 2a2 * -10ab3) + 5a2 * (-5ab3 + 2a2)) = 0
((50a2b6 + -20a3b3) + 5a2 * (-5ab3 + 2a2)) = 0
(50a2b6 + -20a3b3 + (-5ab3 * 5a2 + 2a2 * 5a2)) = 0
(50a2b6 + -20a3b3 + (-25a3b3 + 10a4)) = 0

Combine like terms: -20a3b3 + -25a3b3 = -45a3b3
(50a2b6 + -45a3b3 + 10a4) = 0

Solving
50a2b6 + -45a3b3 + 10a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5a2'.
5a2(10b6 + -9ab3 + 2a2) = 0

Factor a trinomial.
5a2((2b3 + -1a)(5b3 + -2a)) = 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 '(2b3 + -1a)' equal to zero and attempt to solve:

Simplifying
2b3 + -1a = 0

Reorder the terms:
-1a + 2b3 = 0

Solving
-1a + 2b3 = 0

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

Add '-2b3' to each side of the equation.
-1a + 2b3 + -2b3 = 0 + -2b3

Combine like terms: 2b3 + -2b3 = 0
-1a + 0 = 0 + -2b3
-1a = 0 + -2b3
Remove the zero:
-1a = -2b3

Divide each side by '-1'.
a = 2b3

Simplifying
a = 2b3

Subproblem 3
Set the factor '(5b3 + -2a)' equal to zero and attempt to solve:

Simplifying
5b3 + -2a = 0

Reorder the terms:
-2a + 5b3 = 0

Solving
-2a + 5b3 = 0

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

Add '-5b3' to each side of the equation.
-2a + 5b3 + -5b3 = 0 + -5b3

Combine like terms: 5b3 + -5b3 = 0
-2a + 0 = 0 + -5b3
-2a = 0 + -5b3
Remove the zero:
-2a = -5b3

Divide each side by '-2'.
a = 2.5b3

Simplifying
a = 2.5b3
Solution
a = {0, 2b3, 2.5b3}

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