(s+7)(s+3)=12

Solution for (s+7)(s+3)=12 equation:

Simplifying
(s + 7)(s + 3) = 12

Reorder the terms:
(7 + s)(s + 3) = 12

Reorder the terms:
(7 + s)(3 + s) = 12

Multiply (7 + s) * (3 + s)
(7(3 + s) + s(3 + s)) = 12
((3 * 7 + s * 7) + s(3 + s)) = 12
((21 + 7s) + s(3 + s)) = 12
(21 + 7s + (3 * s + s * s)) = 12
(21 + 7s + (3s + s2)) = 12

Combine like terms: 7s + 3s = 10s
(21 + 10s + s2) = 12

Solving
21 + 10s + s2 = 12

Solving for variable 's'.

Reorder the terms:
21 + -12 + 10s + s2 = 12 + -12

Combine like terms: 21 + -12 = 9
9 + 10s + s2 = 12 + -12

Combine like terms: 12 + -12 = 0
9 + 10s + s2 = 0

Factor a trinomial.
(9 + s)(1 + s) = 0

Subproblem 1
Set the factor '(9 + s)' equal to zero and attempt to solve:

Simplifying
9 + s = 0

Solving
9 + s = 0

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

Add '-9' to each side of the equation.
9 + -9 + s = 0 + -9

Combine like terms: 9 + -9 = 0
0 + s = 0 + -9
s = 0 + -9

Combine like terms: 0 + -9 = -9
s = -9

Simplifying
s = -9
Subproblem 2
Set the factor '(1 + s)' equal to zero and attempt to solve:

Simplifying
1 + s = 0

Solving
1 + s = 0

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

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

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

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

Simplifying
s = -1
Solution
s = {-9, -1}