a^2+5ab-6b^2=0

Solution for a^2+5ab-6b^2=0 equation:

Simplifying
a2 + 5ab + -6b2 = 0

Reorder the terms:
5ab + a2 + -6b2 = 0

Solving
5ab + a2 + -6b2 = 0

Solving for variable 'a'.

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

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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

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

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

Simplifying
a + 6b = 0

Solving
a + 6b = 0

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

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

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

Simplifying
a = -6b
Solution
a = {b, -6b}