b^2=5b-4

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

Simplifying
b2 = 5b + -4

Reorder the terms:
b2 = -4 + 5b

Solving
b2 = -4 + 5b

Solving for variable 'b'.

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

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

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

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

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

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

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

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

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

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

Simplifying
b = 4
Solution
b = {1, 4}