a^2-ab-42b^2=0

Solution for a^2-ab-42b^2=0 equation:

Simplifying
a2 + -1ab + -42b2 = 0

Reorder the terms:
-1ab + a2 + -42b2 = 0

Solving
-1ab + a2 + -42b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -7b)(a + 6b) = 0

Subproblem 1
Set the factor '(a + -7b)' equal to zero and attempt to solve:

Simplifying
a + -7b = 0

Solving
a + -7b = 0

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

Add '7b' to each side of the equation.
a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
a + 0 = 0 + 7b
a = 0 + 7b
Remove the zero:
a = 7b

Simplifying
a = 7b
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 = {7b, -6b}