4b^2=5b-1

Solution for 4b^2=5b-1 equation:

Simplifying
4b2 = 5b + -1

Reorder the terms:
4b2 = -1 + 5b

Solving
4b2 = -1 + 5b

Solving for variable 'b'.

Reorder the terms:
1 + -5b + 4b2 = -1 + 5b + 1 + -5b

Reorder the terms:
1 + -5b + 4b2 = -1 + 1 + 5b + -5b

Combine like terms: -1 + 1 = 0
1 + -5b + 4b2 = 0 + 5b + -5b
1 + -5b + 4b2 = 5b + -5b

Combine like terms: 5b + -5b = 0
1 + -5b + 4b2 = 0

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

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

Simplifying
1 + -4b = 0

Solving
1 + -4b = 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 + -4b = 0 + -1

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

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

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

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

Simplifying
1 + -1b = 0

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

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

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

Divide each side by '-1'.
b = 1

Simplifying
b = 1
Solution
b = {0.25, 1}