8a^2-46ab-70b^2=0

Solution for 8a^2-46ab-70b^2=0 equation:

Simplifying
8a2 + -46ab + -70b2 = 0

Reorder the terms:
-46ab + 8a2 + -70b2 = 0

Solving
-46ab + 8a2 + -70b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-23ab + 4a2 + -35b2) = 0

Factor a trinomial.
2((a + -7b)(4a + 5b)) = 0

Ignore the factor 2.
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 '(4a + 5b)' equal to zero and attempt to solve:

Simplifying
4a + 5b = 0

Solving
4a + 5b = 0

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

Add '-5b' to each side of the equation.
4a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
4a + 0 = 0 + -5b
4a = 0 + -5b
Remove the zero:
4a = -5b

Divide each side by '4'.
a = -1.25b

Simplifying
a = -1.25b
Solution
a = {7b, -1.25b}