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

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

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

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

Reorder the terms:
((ab + 3a2) + 3b * (3a + b)) = 0
((ab + 3a2) + 3b * (3a + b)) = 0
(ab + 3a2 + (3a * 3b + b * 3b)) = 0
(ab + 3a2 + (9ab + 3b2)) = 0

Reorder the terms:
(ab + 9ab + 3a2 + 3b2) = 0

Combine like terms: ab + 9ab = 10ab
(10ab + 3a2 + 3b2) = 0

Solving
10ab + 3a2 + 3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + b)(a + 3b) = 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 + 3b)' equal to zero and attempt to solve:

Simplifying
a + 3b = 0

Solving
a + 3b = 0

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

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

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

Simplifying
a = -3b
Solution
a = {-0.3333333333b, -3b}