The given equation is:

4tg^2 (x) - 3/(sin (3pi/2+x)) +3 = 0

Let's simplify the expression step by step:

Rewrite the tangent function as sine and cosine:
4(tg x)^2 = 4(sin x / cos x)^2 = 4(sin^2 x / cos^2 x)

Replace sine and cosine with their respective identities:
4(sin^2 x / cos^2 x) - 3/(sin (3pi/2+x)) + 3 = 0

Use Pythagorean identity to simplify the expression:
4(1 - cos^2 x) - 3/(sin(x + pi/2)) + 3 = 0
4 - 4cos^2 x - 3/cos x + 3 = 0

Multiply through by cos x to eliminate the fraction:
4cos x - 4cos^3 x - 3 + 3cos x = 0
4cos x + 3cos x - 4cos^3 x = 0
7cos x - 4cos^3 x = 0

This equation can be further simplified or solved depending on the context or requirements of the problem.