(4x-5)(4x+5)-(4x+5)-(4x+1)(3x-8)<15x-27

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Expanding the first two terms:

(4x - 5)(4x + 5) = 16x^2 - 20x + 20x - 25 = 16x^2 - 25

Expanding the last two terms:

-(4x + 5) = -4x - 5

(4x + 1)(3x - 8) = 12x^2 - 32x + 3x - 8 = 12x^2 - 29x - 8

Putting it all together:

(16x^2 - 25) - (4x + 5) - (12x^2 - 29x - 8) < 15x - 27
16x^2 - 25 - 4x - 5 - 12x^2 + 29x + 8 < 15x - 27
4x^2 + 20x - 22 < 15x - 27
4x^2 + 20x - 15x + 27 - 22 < 0
4x^2 + 5x + 5 < 0

Unfortunately, this inequality does not factor easily, so we can try to analyze it by finding the roots of the equation 4x^2 + 5x + 5 = 0 using the quadratic formula:

x = (-B ± sqrt(B^2 - 4AC)) / 2A
x = (-5 ± sqrt(5^2 - 445)) / 2*4
x = (-5 ± sqrt(25 - 80)) / 8
x = (-5 ± sqrt(-55)) / 8
x = (-5 ± i√55) / 8

Since the discriminant is negative, the roots are complex. Therefore, the inequality 4x^2 + 5x + 5 < 0 has no real solutions, and the original inequality does not hold for any real values of x.