b^2=b+42

Solution for b^2=b+42 equation:

Simplifying
b2 = b + 42

Reorder the terms:
b2 = 42 + b

Solving
b2 = 42 + b

Solving for variable 'b'.

Reorder the terms:
-42 + -1b + b2 = 42 + b + -42 + -1b

Reorder the terms:
-42 + -1b + b2 = 42 + -42 + b + -1b

Combine like terms: 42 + -42 = 0
-42 + -1b + b2 = 0 + b + -1b
-42 + -1b + b2 = b + -1b

Combine like terms: b + -1b = 0
-42 + -1b + b2 = 0

Factor a trinomial.
(-6 + -1b)(7 + -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 '(7 + -1b)' equal to zero and attempt to solve:

Simplifying
7 + -1b = 0

Solving
7 + -1b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1b = 0 + -7
-1b = 0 + -7

Combine like terms: 0 + -7 = -7
-1b = -7

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Solution
b = {-6, 7}