Can you please show your work and explain this math

1: x^2 + 3x - 18 = 0

a. Solve by factoring.
b. Solve using the quadratic formula.

2: x^2 + 4x - 21 = 0

a. Solve by factoring.
b. Solve using the quadratic formula.

3: x^2 + 2x - 15 = 0

a. Solve by factoring.
b. Solve using the quadratic formula.

Did you learn FOIL? If the equation looks like Ax^2 + Bx + C = 0, where A is 1, BC are any numbers, and the signs can be addition/subtraction, normally you can find two numbers that multiply to get C, then with the same two numbers, they can be added to get B.
For number 1:
6 * -3 = -18, and 6 - 3 = 3
(x+6)(x-3) , the answers are numbers that make the equation = 0, so x=-6, and x=+3.
If you cannot find two numbers that multiply to get C or added to B, then you use the quadratic formula
I assume you know the quadratic formula, google the quadratic formula if you don't know it.
Just plug in A, B, C.
For number 1, A = 1, B= +3, C=-18.
Solve the quadratic formula, you'll get
(-3 + SqRt( 9 + 72 ))/2 = 3
(-3 - SqRt( 9 + 72 ))/2 = -6
The same answers we got from factoring

factoring:
because you have no coefficient in these problems for the x^2,
(x+- number)(x+- number)
the factors of the last number have to be added or subtracted to get the middle cofficient.
number 1.
(x+6)(x-6)

quadratic:
i assume you have the quadratic formula, so just plug it in.
-3 +- SR[9-4(1)(18)]
-3 +- SR[-31]
over 2a

answer:
-3 +- i radical 31
and put that over 2