(a-b)(a-3b)=0

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

Simplifying
(a + -1b)(a + -3b) = 0

Multiply (a + -1b) * (a + -3b)
(a(a + -3b) + -1b * (a + -3b)) = 0
((a * a + -3b * a) + -1b * (a + -3b)) = 0

Reorder the terms:
((-3ab + a2) + -1b * (a + -3b)) = 0
((-3ab + a2) + -1b * (a + -3b)) = 0
(-3ab + a2 + (a * -1b + -3b * -1b)) = 0
(-3ab + a2 + (-1ab + 3b2)) = 0

Reorder the terms:
(-3ab + -1ab + a2 + 3b2) = 0

Combine like terms: -3ab + -1ab = -4ab
(-4ab + a2 + 3b2) = 0

Solving
-4ab + a2 + 3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -3b)(a + -1b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(a + -1b)' equal to zero and attempt to solve:

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

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

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