48a^2-8ab-b^2=0

Solution for 48a^2-8ab-b^2=0 equation:

Simplifying
48a2 + -8ab + -1b2 = 0

Reorder the terms:
-8ab + 48a2 + -1b2 = 0

Solving
-8ab + 48a2 + -1b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -1b)(12a + b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(12a + b)' equal to zero and attempt to solve:

Simplifying
12a + b = 0

Solving
12a + b = 0

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

Add '-1b' to each side of the equation.
12a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
12a + 0 = 0 + -1b
12a = 0 + -1b
Remove the zero:
12a = -1b

Divide each side by '12'.
a = -0.08333333333b

Simplifying
a = -0.08333333333b
Solution
a = {0.25b, -0.08333333333b}