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 = -14
-14 + -2s + 8s2 = 1

Solving
-14 + -2s + 8s2 = 1

Solving for variable 's'.

Reorder the terms:
-14 + -1 + -2s + 8s2 = 1 + -1

Combine like terms: -14 + -1 = -15
-15 + -2s + 8s2 = 1 + -1

Combine like terms: 1 + -1 = 0
-15 + -2s + 8s2 = 0

Factor a trinomial.
(-5 + -4s)(3 + -2s) = 0

Subproblem 1
Set the factor '(-5 + -4s)' equal to zero and attempt to solve:

Simplifying
-5 + -4s = 0

Solving
-5 + -4s = 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 + -4s = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4s = 0 + 5
-4s = 0 + 5

Combine like terms: 0 + 5 = 5
-4s = 5

Divide each side by '-4'.
s = -1.25

Simplifying
s = -1.25
Subproblem 2
Set the factor '(3 + -2s)' equal to zero and attempt to solve:

Simplifying
3 + -2s = 0

Solving
3 + -2s = 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 + -2s = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2s = 0 + -3
-2s = 0 + -3

Combine like terms: 0 + -3 = -3
-2s = -3

Divide each side by '-2'.
s = 1.5

Simplifying
s = 1.5
Solution
s = {-1.25, 1.5}