192=(14+s)(10+s)

Solution for 192=(14+s)(10+s) equation:

Simplifying
192 = (14 + s)(10 + s)

Multiply (14 + s) * (10 + s)
192 = (14(10 + s) + s(10 + s))
192 = ((10 * 14 + s * 14) + s(10 + s))
192 = ((140 + 14s) + s(10 + s))
192 = (140 + 14s + (10 * s + s * s))
192 = (140 + 14s + (10s + s2))

Combine like terms: 14s + 10s = 24s
192 = (140 + 24s + s2)

Solving
192 = 140 + 24s + s2

Solving for variable 's'.

Combine like terms: 192 + -140 = 52
52 + -24s + -1s2 = 140 + 24s + s2 + -140 + -24s + -1s2

Reorder the terms:
52 + -24s + -1s2 = 140 + -140 + 24s + -24s + s2 + -1s2

Combine like terms: 140 + -140 = 0
52 + -24s + -1s2 = 0 + 24s + -24s + s2 + -1s2
52 + -24s + -1s2 = 24s + -24s + s2 + -1s2

Combine like terms: 24s + -24s = 0
52 + -24s + -1s2 = 0 + s2 + -1s2
52 + -24s + -1s2 = s2 + -1s2

Combine like terms: s2 + -1s2 = 0
52 + -24s + -1s2 = 0

Factor a trinomial.
(2 + -1s)(26 + s) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(26 + s)' equal to zero and attempt to solve:

Simplifying
26 + s = 0

Solving
26 + s = 0

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

Add '-26' to each side of the equation.
26 + -26 + s = 0 + -26

Combine like terms: 26 + -26 = 0
0 + s = 0 + -26
s = 0 + -26

Combine like terms: 0 + -26 = -26
s = -26

Simplifying
s = -26
Solution
s = {2, -26}