8b^2=2b+3

Solution for 8b^2=2b+3 equation:

Simplifying
8b2 = 2b + 3

Reorder the terms:
8b2 = 3 + 2b

Solving
8b2 = 3 + 2b

Solving for variable 'b'.

Reorder the terms:
-3 + -2b + 8b2 = 3 + 2b + -3 + -2b

Reorder the terms:
-3 + -2b + 8b2 = 3 + -3 + 2b + -2b

Combine like terms: 3 + -3 = 0
-3 + -2b + 8b2 = 0 + 2b + -2b
-3 + -2b + 8b2 = 2b + -2b

Combine like terms: 2b + -2b = 0
-3 + -2b + 8b2 = 0

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

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

Simplifying
-1 + -2b = 0

Solving
-1 + -2b = 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 + -2b = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2b = 0 + 1
-2b = 0 + 1

Combine like terms: 0 + 1 = 1
-2b = 1

Divide each side by '-2'.
b = -0.5

Simplifying
b = -0.5
Subproblem 2
Set the factor '(3 + -4b)' equal to zero and attempt to solve:

Simplifying
3 + -4b = 0

Solving
3 + -4b = 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 + -4b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4b = 0 + -3
-4b = 0 + -3

Combine like terms: 0 + -3 = -3
-4b = -3

Divide each side by '-4'.
b = 0.75

Simplifying
b = 0.75
Solution
b = {-0.5, 0.75}