168(V - 4) + 4(V^2 - 16) + 48(V + 4) = 30(V^2 - 16)

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Let's simplify the given equation step by step:

168(V - 4) + 4(V^2 - 16) + 48(V + 4) = 30(V^2 - 16)

Expand each term:

168V - 672 + 4V^2 - 64 + 48V + 192 = 30V^2 - 480

Combine like terms:

4V^2 + 216V - 544 = 30V^2 - 480

Rearrange the terms:

4V^2 - 30V^2 + 216V - 480 + 544 = 0

-26V^2 + 216V + 64 = 0

Now, we have a quadratic equation. To solve for V, we can use the quadratic formula:

V = (-B ± √(B^2 - 4AC)) / 2A

Where A = -26, B = 216, and C = 64.

V = (-216 ± √(216^2 - 4(-26)(64))) / 2(-26)

V = (-216 ± √(46656 + 6656)) / -52

V = (-216 ± √(53312)) / -52

V = (-216 ± 230.95) / -52

V = (-446.95 / -52) or (14.95 / -52)

V = 8.59 or -0.29

Therefore, the solutions to the equation are V = 8.59 or V = -0.29.