(15s^2+5s-13)+(-14s^2-10s+8)=1

Solution for (15s^2+5s-13)+(-14s^2-10s+8)=1 equation:

Simplifying
(15s2 + 5s + -13) + (-14s2 + -10s + 8) = 1

Reorder the terms:
(-13 + 5s + 15s2) + (-14s2 + -10s + 8) = 1

Remove parenthesis around (-13 + 5s + 15s2)
-13 + 5s + 15s2 + (-14s2 + -10s + 8) = 1

Reorder the terms:
-13 + 5s + 15s2 + (8 + -10s + -14s2) = 1

Remove parenthesis around (8 + -10s + -14s2)
-13 + 5s + 15s2 + 8 + -10s + -14s2 = 1

Reorder the terms:
-13 + 8 + 5s + -10s + 15s2 + -14s2 = 1

Combine like terms: -13 + 8 = -5
-5 + 5s + -10s + 15s2 + -14s2 = 1

Combine like terms: 5s + -10s = -5s
-5 + -5s + 15s2 + -14s2 = 1

Combine like terms: 15s2 + -14s2 = 1s2
-5 + -5s + 1s2 = 1

Solving
-5 + -5s + 1s2 = 1

Solving for variable 's'.

Reorder the terms:
-5 + -1 + -5s + 1s2 = 1 + -1

Combine like terms: -5 + -1 = -6
-6 + -5s + 1s2 = 1 + -1

Combine like terms: 1 + -1 = 0
-6 + -5s + 1s2 = 0

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

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

Simplifying
-1 + -1s = 0

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

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

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

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

Simplifying
s = -1
Subproblem 2
Set the factor '(6 + -1s)' equal to zero and attempt to solve:

Simplifying
6 + -1s = 0

Solving
6 + -1s = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1s = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1s = 0 + -6
-1s = 0 + -6

Combine like terms: 0 + -6 = -6
-1s = -6

Divide each side by '-1'.
s = 6

Simplifying
s = 6
Solution
s = {-1, 6}