(a+b)(3ab+b^2)=0

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


Simplifying
(a + b)(3ab + b2) = 0

Multiply (a + b) * (3ab + b2)
(a(3ab + b2) + b(3ab + b2)) = 0
((3ab * a + b2 * a) + b(3ab + b2)) = 0

Reorder the terms:
((ab2 + 3a2b) + b(3ab + b2)) = 0
((ab2 + 3a2b) + b(3ab + b2)) = 0
(ab2 + 3a2b + (3ab * b + b2 * b)) = 0
(ab2 + 3a2b + (3ab2 + b3)) = 0

Reorder the terms:
(ab2 + 3ab2 + 3a2b + b3) = 0

Combine like terms: ab2 + 3ab2 = 4ab2
(4ab2 + 3a2b + b3) = 0

Solving
4ab2 + 3a2b + b3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'b'.
b(4ab + 3a2 + b2) = 0

Factor a trinomial.
b((3a + b)(a + b)) = 0


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

Simplifying
b = 0

Solving
b = 0

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

Add '-1b' to each side of the equation.
b + -1b = 0 + -1b
Remove the zero:
0 = -1b

Simplifying
0 = -1b

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 '(3a + b)' equal to zero and attempt to solve:

Simplifying
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 '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

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

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

Simplifying
a = -1b
Solution
a = {-0.3333333333b, -1b}

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