(a+b)(3a+b)=0

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

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

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

Reorder the terms:
((ab + 3a2) + b(3a + b)) = 0
((ab + 3a2) + b(3a + b)) = 0
(ab + 3a2 + (3a * b + b * b)) = 0
(ab + 3a2 + (3ab + b2)) = 0

Reorder the terms:
(ab + 3ab + 3a2 + b2) = 0

Combine like terms: ab + 3ab = 4ab
(4ab + 3a2 + b2) = 0

Solving
4ab + 3a2 + b2 = 0

Solving for variable 'a'.

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

Subproblem 1
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 2
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}