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

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

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

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

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

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

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

Solving
a2 + -9b2 = 0

Solving for variable 'a'.

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

Add '9b2' to each side of the equation.
a2 + -9b2 + 9b2 = 0 + 9b2

Combine like terms: -9b2 + 9b2 = 0
a2 + 0 = 0 + 9b2
a2 = 0 + 9b2
Remove the zero:
a2 = 9b2

Simplifying
a2 = 9b2

Take the square root of each side:
a = {-3b, 3b}