6a^2-12ab+6b^2=0

Solution for 6a^2-12ab+6b^2=0 equation:

Simplifying
6a2 + -12ab + 6b2 = 0

Reorder the terms:
-12ab + 6a2 + 6b2 = 0

Solving
-12ab + 6a2 + 6b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2ab + a2 + b2) = 0

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

Ignore the factor 6.
Subproblem 1
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
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 = {b, b}