0=s^2+12s+35

Solution for 0=s^2+12s+35 equation:

Simplifying
0 = s2 + 12s + 35

Reorder the terms:
0 = 35 + 12s + s2

Solving
0 = 35 + 12s + s2

Solving for variable 's'.

Combine like terms: 0 + -35 = -35
-35 + -12s + -1s2 = 35 + 12s + s2 + -35 + -12s + -1s2

Reorder the terms:
-35 + -12s + -1s2 = 35 + -35 + 12s + -12s + s2 + -1s2

Combine like terms: 35 + -35 = 0
-35 + -12s + -1s2 = 0 + 12s + -12s + s2 + -1s2
-35 + -12s + -1s2 = 12s + -12s + s2 + -1s2

Combine like terms: 12s + -12s = 0
-35 + -12s + -1s2 = 0 + s2 + -1s2
-35 + -12s + -1s2 = s2 + -1s2

Combine like terms: s2 + -1s2 = 0
-35 + -12s + -1s2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 12s + s2) = 0

Factor a trinomial.
-1((7 + s)(5 + s)) = 0

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

Simplifying
7 + s = 0

Solving
7 + s = 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 + s = 0 + -7

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

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

Simplifying
s = -7
Subproblem 2
Set the factor '(5 + s)' equal to zero and attempt to solve:

Simplifying
5 + s = 0

Solving
5 + s = 0

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

Add '-5' to each side of the equation.
5 + -5 + s = 0 + -5

Combine like terms: 5 + -5 = 0
0 + s = 0 + -5
s = 0 + -5

Combine like terms: 0 + -5 = -5
s = -5

Simplifying
s = -5
Solution
s = {-7, -5}