0=s^2-s-42

Solution for 0=s^2-s-42 equation:

Simplifying
0 = s2 + -1s + -42

Reorder the terms:
0 = -42 + -1s + s2

Solving
0 = -42 + -1s + s2

Solving for variable 's'.

Combine like terms: 0 + 42 = 42
42 + s + -1s2 = -42 + -1s + s2 + 42 + s + -1s2

Reorder the terms:
42 + s + -1s2 = -42 + 42 + -1s + s + s2 + -1s2

Combine like terms: -42 + 42 = 0
42 + s + -1s2 = 0 + -1s + s + s2 + -1s2
42 + s + -1s2 = -1s + s + s2 + -1s2

Combine like terms: -1s + s = 0
42 + s + -1s2 = 0 + s2 + -1s2
42 + s + -1s2 = s2 + -1s2

Combine like terms: s2 + -1s2 = 0
42 + s + -1s2 = 0

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

Subproblem 1
Set the factor '(7 + -1s)' equal to zero and attempt to solve:

Simplifying
7 + -1s = 0

Solving
7 + -1s = 0

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

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

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

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

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

Simplifying
s = 7
Subproblem 2
Set the factor '(6 + s)' equal to zero and attempt to solve:

Simplifying
6 + s = 0

Solving
6 + s = 0

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

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

Combine like terms: 6 + -6 = 0
0 + s = 0 + -6
s = 0 + -6

Combine like terms: 0 + -6 = -6
s = -6

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