8v^2+26vb-7b^2=0

Solution for 8v^2+26vb-7b^2=0 equation:

Simplifying
8v2 + 26vb + -7b2 = 0

Reorder the terms:
26bv + -7b2 + 8v2 = 0

Solving
26bv + -7b2 + 8v2 = 0

Solving for variable 'b'.

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

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

Simplifying
-7b + -2v = 0

Solving
-7b + -2v = 0

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

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

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

Divide each side by '-7'.
b = -0.2857142857v

Simplifying
b = -0.2857142857v
Subproblem 2
Set the factor '(b + -4v)' equal to zero and attempt to solve:

Simplifying
b + -4v = 0

Solving
b + -4v = 0

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

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

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

Simplifying
b = 4v
Solution
b = {-0.2857142857v, 4v}