b^2=14b-48

Solution for b^2=14b-48 equation:

Simplifying
b2 = 14b + -48

Reorder the terms:
b2 = -48 + 14b

Solving
b2 = -48 + 14b

Solving for variable 'b'.

Reorder the terms:
48 + -14b + b2 = -48 + 14b + 48 + -14b

Reorder the terms:
48 + -14b + b2 = -48 + 48 + 14b + -14b

Combine like terms: -48 + 48 = 0
48 + -14b + b2 = 0 + 14b + -14b
48 + -14b + b2 = 14b + -14b

Combine like terms: 14b + -14b = 0
48 + -14b + b2 = 0

Factor a trinomial.
(6 + -1b)(8 + -1b) = 0

Subproblem 1
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Subproblem 2
Set the factor '(8 + -1b)' equal to zero and attempt to solve:

Simplifying
8 + -1b = 0

Solving
8 + -1b = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1b = 0 + -8
-1b = 0 + -8

Combine like terms: 0 + -8 = -8
-1b = -8

Divide each side by '-1'.
b = 8

Simplifying
b = 8
Solution
b = {6, 8}