6a^2+-50ab+16b^2=0

Solution for 6a^2+-50ab+16b^2=0 equation:

Simplifying
6a2 + -50ab + 16b2 = 0

Reorder the terms:
-50ab + 6a2 + 16b2 = 0

Solving
-50ab + 6a2 + 16b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25ab + 3a2 + 8b2) = 0

Factor a trinomial.
2((a + -8b)(3a + -1b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(a + -8b)' equal to zero and attempt to solve:

Simplifying
a + -8b = 0

Solving
a + -8b = 0

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

Add '8b' to each side of the equation.
a + -8b + 8b = 0 + 8b

Combine like terms: -8b + 8b = 0
a + 0 = 0 + 8b
a = 0 + 8b
Remove the zero:
a = 8b

Simplifying
a = 8b
Subproblem 2
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
Solution
a = {8b, 0.3333333333b}