To solve this trigonometric equation, we will use the properties of sin and cos functions.

Given: sin(4π - x) - cos(3π/2 + x) + 1 = 0

Recall the trigonometric identities:
a) sin(π/2 + θ) = cos(θ)
b) cos(π + θ) = -cos(θ)
c) sin(2π - θ) = sin(θ)

Substitute sin(4π - x) using identity c:
sin(4π - x) = sin(x)

Substitute cos(3π/2 + x) using identity a:
cos(3π/2 + x) = sin(x)

Substituting these values into the equation:
sin(x) - sin(x) + 1 = 0
0 + 1 = 0
1 = 0

Since the equation produced a contradiction, the original trigonometric equation sin(4π - x) - cos(3π/2 + x) + 1 = 0 has no solutions.