12a^2-7ab+b^2=0

Solution for 12a^2-7ab+b^2=0 equation:

Simplifying
12a2 + -7ab + b2 = 0

Reorder the terms:
-7ab + 12a2 + b2 = 0

Solving
-7ab + 12a2 + b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -1b)(4a + -1b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4a + -1b)' equal to zero and attempt to solve:

Simplifying
4a + -1b = 0

Solving
4a + -1b = 0

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

Add 'b' to each side of the equation.
4a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
4a + 0 = 0 + b
4a = 0 + b
Remove the zero:
4a = b

Divide each side by '4'.
a = 0.25b

Simplifying
a = 0.25b
Solution
a = {0.3333333333b, 0.25b}