8a^2-2ab-21b^2=0

Solution for 8a^2-2ab-21b^2=0 equation:

Simplifying
8a2 + -2ab + -21b2 = 0

Reorder the terms:
-2ab + 8a2 + -21b2 = 0

Solving
-2ab + 8a2 + -21b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -7b)(2a + 3b) = 0

Subproblem 1
Set the factor '(4a + -7b)' equal to zero and attempt to solve:

Simplifying
4a + -7b = 0

Solving
4a + -7b = 0

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

Add '7b' to each side of the equation.
4a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
4a + 0 = 0 + 7b
4a = 0 + 7b
Remove the zero:
4a = 7b

Divide each side by '4'.
a = 1.75b

Simplifying
a = 1.75b
Subproblem 2
Set the factor '(2a + 3b)' equal to zero and attempt to solve:

Simplifying
2a + 3b = 0

Solving
2a + 3b = 0

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

Add '-3b' to each side of the equation.
2a + 3b + -3b = 0 + -3b

Combine like terms: 3b + -3b = 0
2a + 0 = 0 + -3b
2a = 0 + -3b
Remove the zero:
2a = -3b

Divide each side by '2'.
a = -1.5b

Simplifying
a = -1.5b
Solution
a = {1.75b, -1.5b}