8a^2-20ab-28b^2=0

Solution for 8a^2-20ab-28b^2=0 equation:

Simplifying
8a2 + -20ab + -28b2 = 0

Reorder the terms:
-20ab + 8a2 + -28b2 = 0

Solving
-20ab + 8a2 + -28b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5ab + 2a2 + -7b2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(2a + -7b)' equal to zero and attempt to solve:

Simplifying
2a + -7b = 0

Solving
2a + -7b = 0

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

Add '7b' to each side of the equation.
2a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
2a + 0 = 0 + 7b
2a = 0 + 7b
Remove the zero:
2a = 7b

Divide each side by '2'.
a = 3.5b

Simplifying
a = 3.5b
Subproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

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

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

Simplifying
a = -1b
Solution
a = {3.5b, -1b}