**Solution:**

To find the value of B in the equation B^2 + 3B - 24 = 0, we can use the quadratic formula or factorization method. Let's solve it using both methods:

**1. Using the Quadratic Formula:**

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation B^2 + 3B - 24 = 0, the coefficients are:
a = 1, b = 3, and c = -24.

Plugging these values into the quadratic formula, we get:

B = (-3 ± √(3^2 - 4(1)(-24))) / (2(1))

Simplifying further:

B = (-3 ± √(9 + 96)) / 2

B = (-3 ± √105) / 2

Therefore, the solutions for B are:

B = (-3 + √105) / 2 and B = (-3 - √105) / 2

**2. Using Factorization Method:**

To solve the equation B^2 + 3B - 24 = 0 using factorization, we need to find two numbers whose product is -24 and whose sum is 3.

Let's try different pairs of factors of -24 until we find the pair whose sum is 3:

-24 = 1 × (-24) --> Sum = 1 - 24 = -23
-24 = 2 × (-12) --> Sum = 2 - 12 = -10
-24 = 3 × (-8) --> Sum = 3 - 8 = -5
-24 = 4 × (-6) --> Sum = 4 - 6 = -2
-24 = -1 × 24 --> Sum = -1 + 24 = 23
-24 = -2 × 12 --> Sum = -2 + 12 = 10
-24 = -3 × 8 --> Sum = -3 + 8 = 5
-24 = -4 × 6 --> Sum = -4 + 6 = 2

From the pairs above, we can see that -3 and 8 have a sum of 5, which matches the coefficient of B in the equation.

Therefore, we can rewrite the equation as:

B^2 + 3B - 24 = (B - 3)(B + 8) = 0

Setting each factor equal to zero, we get:

B - 3 = 0 --> B = 3
B + 8 = 0 --> B = -8

Therefore, the solutions for B are:

B = 3 and B = -8

In conclusion, the solutions for B in the equation B^2 + 3B - 24 = 0 are B = 3, B = -8, B = (-3 + √105) / 2, and B = (-3 - √105) / 2.