6(s+1)(s+1)-17(s+1)=3

Solution for 6(s+1)(s+1)-17(s+1)=3 equation:

Simplifying
6(s + 1)(s + 1) + -17(s + 1) = 3

Reorder the terms:
6(1 + s)(s + 1) + -17(s + 1) = 3

Reorder the terms:
6(1 + s)(1 + s) + -17(s + 1) = 3

Multiply (1 + s) * (1 + s)
6(1(1 + s) + s(1 + s)) + -17(s + 1) = 3
6((1 * 1 + s * 1) + s(1 + s)) + -17(s + 1) = 3
6((1 + 1s) + s(1 + s)) + -17(s + 1) = 3
6(1 + 1s + (1 * s + s * s)) + -17(s + 1) = 3
6(1 + 1s + (1s + s2)) + -17(s + 1) = 3

Combine like terms: 1s + 1s = 2s
6(1 + 2s + s2) + -17(s + 1) = 3
(1 * 6 + 2s * 6 + s2 * 6) + -17(s + 1) = 3
(6 + 12s + 6s2) + -17(s + 1) = 3

Reorder the terms:
6 + 12s + 6s2 + -17(1 + s) = 3
6 + 12s + 6s2 + (1 * -17 + s * -17) = 3
6 + 12s + 6s2 + (-17 + -17s) = 3

Reorder the terms:
6 + -17 + 12s + -17s + 6s2 = 3

Combine like terms: 6 + -17 = -11
-11 + 12s + -17s + 6s2 = 3

Combine like terms: 12s + -17s = -5s
-11 + -5s + 6s2 = 3

Solving
-11 + -5s + 6s2 = 3

Solving for variable 's'.

Reorder the terms:
-11 + -3 + -5s + 6s2 = 3 + -3

Combine like terms: -11 + -3 = -14
-14 + -5s + 6s2 = 3 + -3

Combine like terms: 3 + -3 = 0
-14 + -5s + 6s2 = 0

Factor a trinomial.
(-7 + -6s)(2 + -1s) = 0

Subproblem 1
Set the factor '(-7 + -6s)' equal to zero and attempt to solve:

Simplifying
-7 + -6s = 0

Solving
-7 + -6s = 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 + -6s = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6s = 0 + 7
-6s = 0 + 7

Combine like terms: 0 + 7 = 7
-6s = 7

Divide each side by '-6'.
s = -1.166666667

Simplifying
s = -1.166666667
Subproblem 2
Set the factor '(2 + -1s)' equal to zero and attempt to solve:

Simplifying
2 + -1s = 0

Solving
2 + -1s = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1s = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1s = 0 + -2
-1s = 0 + -2

Combine like terms: 0 + -2 = -2
-1s = -2

Divide each side by '-1'.
s = 2

Simplifying
s = 2
Solution
s = {-1.166666667, 2}