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

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

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

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

Reorder the terms:
((-9ab + 3a2) + -1b * (a + -3b)) = 0
((-9ab + 3a2) + -1b * (a + -3b)) = 0
(-9ab + 3a2 + (a * -1b + -3b * -1b)) = 0
(-9ab + 3a2 + (-1ab + 3b2)) = 0

Reorder the terms:
(-9ab + -1ab + 3a2 + 3b2) = 0

Combine like terms: -9ab + -1ab = -10ab
(-10ab + 3a2 + 3b2) = 0

Solving
-10ab + 3a2 + 3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -3b)(3a + -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 '(3a + -1b)' equal to zero and attempt to solve:

Simplifying
3a + -1b = 0

Solving
3a + -1b = 0

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

Add 'b' to each side of the equation.
3a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
3a + 0 = 0 + b
3a = 0 + b
Remove the zero:
3a = b

Divide each side by '3'.
a = 0.3333333333b

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