b^2=42-b

Solution for b^2=42-b equation:

Simplifying
b2 = 42 + -1b

Solving
b2 = 42 + -1b

Solving for variable 'b'.

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

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

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

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

Factor a trinomial.
(-7 + -1b)(6 + -1b) = 0

Subproblem 1
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
Subproblem 2
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
Solution
b = {-7, 6}