b^2+3=5b-3

Solution for b^2+3=5b-3 equation:

Simplifying
b2 + 3 = 5b + -3

Reorder the terms:
3 + b2 = 5b + -3

Reorder the terms:
3 + b2 = -3 + 5b

Solving
3 + b2 = -3 + 5b

Solving for variable 'b'.

Reorder the terms:
3 + 3 + -5b + b2 = -3 + 5b + 3 + -5b

Combine like terms: 3 + 3 = 6
6 + -5b + b2 = -3 + 5b + 3 + -5b

Reorder the terms:
6 + -5b + b2 = -3 + 3 + 5b + -5b

Combine like terms: -3 + 3 = 0
6 + -5b + b2 = 0 + 5b + -5b
6 + -5b + b2 = 5b + -5b

Combine like terms: 5b + -5b = 0
6 + -5b + b2 = 0

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

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

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

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

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

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

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

Simplifying
3 + -1b = 0

Solving
3 + -1b = 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 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {2, 3}