a^2-5ab-24b^2=0

Solution for a^2-5ab-24b^2=0 equation:

Simplifying
a2 + -5ab + -24b2 = 0

Reorder the terms:
-5ab + a2 + -24b2 = 0

Solving
-5ab + a2 + -24b2 = 0

Solving for variable 'a'.

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

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 '(a + 3b)' equal to zero and attempt to solve:

Simplifying
a + 3b = 0

Solving
a + 3b = 0

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

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

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

Simplifying
a = -3b
Solution
a = {8b, -3b}