8b^2x^2-10bx-3=0

Solution for 8b^2x^2-10bx-3=0 equation:

Simplifying
8b2x2 + -10bx + -3 = 0

Reorder the terms:
-3 + -10bx + 8b2x2 = 0

Solving
-3 + -10bx + 8b2x2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -4bx)(3 + -2bx) = 0

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

Simplifying
-1 + -4bx = 0

Solving
-1 + -4bx = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4bx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4bx = 0 + 1
-4bx = 0 + 1

Combine like terms: 0 + 1 = 1
-4bx = 1

Divide each side by '-4x'.
b = -0.25x-1

Simplifying
b = -0.25x-1
Subproblem 2
Set the factor '(3 + -2bx)' equal to zero and attempt to solve:

Simplifying
3 + -2bx = 0

Solving
3 + -2bx = 0

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

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

Combine like terms: 3 + -3 = 0
0 + -2bx = 0 + -3
-2bx = 0 + -3

Combine like terms: 0 + -3 = -3
-2bx = -3

Divide each side by '-2x'.
b = 1.5x-1

Simplifying
b = 1.5x-1
Solution
b = {-0.25x-1, 1.5x-1}