12a^2+35b^2-43ab=0

Solution for 12a^2+35b^2-43ab=0 equation:

Simplifying
12a2 + 35b2 + -43ab = 0

Reorder the terms:
-43ab + 12a2 + 35b2 = 0

Solving
-43ab + 12a2 + 35b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -7b)(4a + -5b) = 0

Subproblem 1
Set the factor '(3a + -7b)' equal to zero and attempt to solve:

Simplifying
3a + -7b = 0

Solving
3a + -7b = 0

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

Add '7b' to each side of the equation.
3a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
3a + 0 = 0 + 7b
3a = 0 + 7b
Remove the zero:
3a = 7b

Divide each side by '3'.
a = 2.333333333b

Simplifying
a = 2.333333333b
Subproblem 2
Set the factor '(4a + -5b)' equal to zero and attempt to solve:

Simplifying
4a + -5b = 0

Solving
4a + -5b = 0

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

Add '5b' to each side of the equation.
4a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
4a + 0 = 0 + 5b
4a = 0 + 5b
Remove the zero:
4a = 5b

Divide each side by '4'.
a = 1.25b

Simplifying
a = 1.25b
Solution
a = {2.333333333b, 1.25b}