To solve for x, we need to simplify the equation first.

23^(x+1) - 92^(x+1) = 92^x - 23^x

Expanding the exponents:

233^x - 922^x = 92^x - 23^x

63^x - 182^x = 92^x - 23^x

Rearranging terms:

63^x + 23^x = 92^x + 182^x

Combining like terms:

83^x = 272^x

Dividing both sides by 3^x and 2^x:

8 = 27(2/3)^x

To solve for x, take the natural logarithm of both sides:

ln(8) = ln(27(2/3)^x)

ln(8) = ln(27) + x*ln(2/3)

ln(8) = ln(27) + x(ln(2) - ln(3))

ln(8) = ln(27) + x(ln(2/3))

ln(8) - ln(27) = x(ln(2/3))

ln(8/27) = x(ln(2/3))

x = ln(8/27) / ln(2/3)

x ≈ -0.9543

Therefore, x is approximately -0.9543.