24a^3b+24a^2b^2+6ab^3=

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Solution for 24a^3b+24a^2b^2+6ab^3= equation: 


Simplifying
24a3b + 24a2b2 + 6ab3 = 0

Reorder the terms:
6ab3 + 24a2b2 + 24a3b = 0

Solving
6ab3 + 24a2b2 + 24a3b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6ab'.
6ab(b2 + 4ab + 4a2) = 0

Factor a trinomial.
6ab((b + 2a)(b + 2a)) = 0

Ignore the factor 6.

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

Simplifying
ab = 0

Solving
ab = 0

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

Simplifying
ab = 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 + 2a)' equal to zero and attempt to solve:

Simplifying
b + 2a = 0

Reorder the terms:
2a + b = 0

Solving
2a + b = 0

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

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

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

Divide each side by '2'.
a = -0.5b

Simplifying
a = -0.5b

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

Simplifying
b + 2a = 0

Reorder the terms:
2a + b = 0

Solving
2a + b = 0

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

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

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

Divide each side by '2'.
a = -0.5b

Simplifying
a = -0.5b
Solution
a = {-0.5b, -0.5b}

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