8(s-1)(s+1)+2(s+3)=1

Solution for 8(s-1)(s+1)+2(s+3)=1 equation:

Simplifying
8(s + -1)(s + 1) + 2(s + 3) = 1

Reorder the terms:
8(-1 + s)(s + 1) + 2(s + 3) = 1

Reorder the terms:
8(-1 + s)(1 + s) + 2(s + 3) = 1

Multiply (-1 + s) * (1 + s)
8(-1(1 + s) + s(1 + s)) + 2(s + 3) = 1
8((1 * -1 + s * -1) + s(1 + s)) + 2(s + 3) = 1
8((-1 + -1s) + s(1 + s)) + 2(s + 3) = 1
8(-1 + -1s + (1 * s + s * s)) + 2(s + 3) = 1
8(-1 + -1s + (1s + s2)) + 2(s + 3) = 1

Combine like terms: -1s + 1s = 0
8(-1 + 0 + s2) + 2(s + 3) = 1
8(-1 + s2) + 2(s + 3) = 1
(-1 * 8 + s2 * 8) + 2(s + 3) = 1
(-8 + 8s2) + 2(s + 3) = 1

Reorder the terms:
-8 + 8s2 + 2(3 + s) = 1
-8 + 8s2 + (3 * 2 + s * 2) = 1
-8 + 8s2 + (6 + 2s) = 1

Reorder the terms:
-8 + 6 + 2s + 8s2 = 1

Combine like terms: -8 + 6 = -2
-2 + 2s + 8s2 = 1

Solving
-2 + 2s + 8s2 = 1

Solving for variable 's'.

Reorder the terms:
-2 + -1 + 2s + 8s2 = 1 + -1

Combine like terms: -2 + -1 = -3
-3 + 2s + 8s2 = 1 + -1

Combine like terms: 1 + -1 = 0
-3 + 2s + 8s2 = 0

Factor a trinomial.
(-3 + -4s)(1 + -2s) = 0

Subproblem 1
Set the factor '(-3 + -4s)' equal to zero and attempt to solve:

Simplifying
-3 + -4s = 0

Solving
-3 + -4s = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4s = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4s = 0 + 3
-4s = 0 + 3

Combine like terms: 0 + 3 = 3
-4s = 3

Divide each side by '-4'.
s = -0.75

Simplifying
s = -0.75
Subproblem 2
Set the factor '(1 + -2s)' equal to zero and attempt to solve:

Simplifying
1 + -2s = 0

Solving
1 + -2s = 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 + -2s = 0 + -1

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

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

Divide each side by '-2'.
s = 0.5

Simplifying
s = 0.5
Solution
s = {-0.75, 0.5}