**Finding B in the equation B^2 + 3B - 18 = 0**

To find the value of B in the given quadratic equation, we can use the method of factorization or the quadratic formula. Let's explore both methods:

**Method 1: Factorization**

To factorize the quadratic equation, we need to find two numbers whose sum is 3 and whose product is -18. Let's list all the possible pairs of numbers:

1, -18
2, -9
3, -6

Out of these pairs, the pair that satisfies the condition of summing up to 3 is 6 and -3. Therefore, we can rewrite the equation as:

(B + 6)(B - 3) = 0

Now, we can set each factor equal to zero:

B + 6 = 0 or B - 3 = 0

Solving these equations, we get:

B = -6 or B = 3

So, the values of B that satisfy the given quadratic equation are -6 and 3.

**Method 2: Quadratic Formula**

The quadratic formula is given by:

B = (-b ± √(b^2 - 4ac)) / (2a)

In the given equation, a = 1, b = 3, and c = -18. Substituting these values into the quadratic formula, we get:

B = (-(3) ± √((3)^2 - 4(1)(-18))) / (2(1))

Simplifying further:

B = (-3 ± √(9 + 72)) / 2

B = (-3 ± √81) / 2

B = (-3 ± 9) / 2

This gives us two solutions:

B = (-3 + 9) / 2 = 6 / 2 = 3

B = (-3 - 9) / 2 = -12 / 2 = -6

Therefore, the values of B that satisfy the given quadratic equation are -6 and 3.

In conclusion, the solutions to the equation B^2 + 3B - 18 = 0 are B = -6 and B = 3.