b^2-12b-42=3

Solution for b^2-12b-42=3 equation:

Simplifying
b2 + -12b + -42 = 3

Reorder the terms:
-42 + -12b + b2 = 3

Solving
-42 + -12b + b2 = 3

Solving for variable 'b'.

Reorder the terms:
-42 + -3 + -12b + b2 = 3 + -3

Combine like terms: -42 + -3 = -45
-45 + -12b + b2 = 3 + -3

Combine like terms: 3 + -3 = 0
-45 + -12b + b2 = 0

Factor a trinomial.
(-3 + -1b)(15 + -1b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(15 + -1b)' equal to zero and attempt to solve:

Simplifying
15 + -1b = 0

Solving
15 + -1b = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1b = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1b = 0 + -15
-1b = 0 + -15

Combine like terms: 0 + -15 = -15
-1b = -15

Divide each side by '-1'.
b = 15

Simplifying
b = 15
Solution
b = {-3, 15}