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A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

To multiply terms with radicals, multiply the coefficients and radicands separately:

3\( \sqrt{4} \) x 5\( \sqrt{6} \)
(3 x 5)\( \sqrt{4 \times 6} \)
15\( \sqrt{24} \)

Now we need to simplify the radical:

15\( \sqrt{24} \)
15\( \sqrt{6 \times 4} \)
15\( \sqrt{6 \times 2^2} \)
(15)(2)\( \sqrt{6} \)
30\( \sqrt{6} \)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{8 x 4}{6 x 4} \) - \( \frac{7 x 3}{8 x 3} \)

\( \frac{32}{24} \) - \( \frac{21}{24} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{32 - 21}{24} \) = \( \frac{11}{24} \) = \(\frac{11}{24}\)

First, solve for \( \left|c + 2\right| \):

\( \left|c + 2\right| \) + 9 = 3
\( \left|c + 2\right| \) = 3 - 9
\( \left|c + 2\right| \) = -6

The value inside the absolute value brackets can be either positive or negative so (c + 2) must equal - 6 or --6 for \( \left|c + 2\right| \) to equal -6:

So, c = 4 or c = -8.