6a^2x^2-abx-5b^2=0

Solution for 6a^2x^2-abx-5b^2=0 equation:

Simplifying
6a2x2 + -1abx + -5b2 = 0

Reorder the terms:
-1abx + 6a2x2 + -5b2 = 0

Solving
-1abx + 6a2x2 + -5b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(ax + -1b)(6ax + 5b) = 0

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

Simplifying
ax + -1b = 0

Solving
ax + -1b = 0

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

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

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

Divide each side by 'x'.
a = bx-1

Simplifying
a = bx-1
Subproblem 2
Set the factor '(6ax + 5b)' equal to zero and attempt to solve:

Simplifying
6ax + 5b = 0

Solving
6ax + 5b = 0

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

Add '-5b' to each side of the equation.
6ax + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
6ax + 0 = 0 + -5b
6ax = 0 + -5b
Remove the zero:
6ax = -5b

Divide each side by '6x'.
a = -0.8333333333bx-1

Simplifying
a = -0.8333333333bx-1
Solution
a = {bx-1, -0.8333333333bx-1}