a^2-8ab+12b^2=0

Solution for a^2-8ab+12b^2=0 equation:

Simplifying
a2 + -8ab + 12b2 = 0

Reorder the terms:
-8ab + a2 + 12b2 = 0

Solving
-8ab + a2 + 12b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -6b)(a + -2b) = 0

Subproblem 1
Set the factor '(a + -6b)' equal to zero and attempt to solve:

Simplifying
a + -6b = 0

Solving
a + -6b = 0

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

Add '6b' to each side of the equation.
a + -6b + 6b = 0 + 6b

Combine like terms: -6b + 6b = 0
a + 0 = 0 + 6b
a = 0 + 6b
Remove the zero:
a = 6b

Simplifying
a = 6b
Subproblem 2
Set the factor '(a + -2b)' equal to zero and attempt to solve:

Simplifying
a + -2b = 0

Solving
a + -2b = 0

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

Add '2b' to each side of the equation.
a + -2b + 2b = 0 + 2b

Combine like terms: -2b + 2b = 0
a + 0 = 0 + 2b
a = 0 + 2b
Remove the zero:
a = 2b

Simplifying
a = 2b
Solution
a = {6b, 2b}