3x squared -16x - 7=5

3x^2 - 16x - 7 = 5.    This is a quadratic equation.  Cross the 5 to the other side.

3x^2 - 16x - 7 - 5 = 0

3x^2 - 16x - 12 = 0.    Let us use factorization method.

Multiply the first coefficient and last term = 3 * -12 = -36.

We think of two numbers that multiply to give -36 and add up to give the middle coefficient -16.

The two numbers  are = 2 and -18.

2 * -18 = -36.
2 + (-18) = -16.

We replace the middle term -16 with 2 +(-18) = 2 - 18.

3x^2 - 16x - 12 = 0

3x^2 + 2x - 18x - 12 = 0      Factorize.

x(3x + 2)  - 6(3x + 2) = 0

(3x + 2) (x -6)  = 0.

Therefore (3x + 2) = 0 or   (x -6) = 0

(3x + 2) = 0                      x - 6 = 0
3x = 0 -2                          x = 0 + 6
3x = -2                             x = 6
x = -2/3 
3x = -2
x = -2/3 
Therefore  x = -2/3  or 6.

One that half its volume