There are multiple ways to solve a quadratic equation. 3 common ways to solve a quadratic equation are by: factoring, completing the square, or using the quadratic formula. I highly recommond simply google searching how to solve a quadratic equation.
However here's an explaination on one of the methods:
Let's solve the quadratic equation using the factoring method: x2 + 2x + 1 = 0.
To factor, you simply try to find the multiples (the factors) of the c-value which is the coefficient of the number most commonly without an x and in this case the c-value is 1. So the factors of 1 are: 1 and 1. Now you do the same for the a-value which is the coefficient of the x2 value. In this case the a-value is also 1. The multiples of 1 are still: 1 and 1. Now you play around the with the factors (multiples) of the a and c value. What you want to do is that you want multiply one a-factor by one c-factor, then do the same for another a and c factor. Mess around with the multiplication until the sum of both products equals the b-value which in this case is 2 (the b-value is the coefficient next to the x). It helps to organize it like so:
1 x 1 = 1
1 x 1 = 1
On the left are the multiples of the a - value and on the right are the multiples of the c-value.
In this equation you don't have to mess around with it much because the sum of the factors already equals the b-value.
1 +1 = 2 (2 is our b-value).
So the factors of this equation are (x+1) (x+1). The solution is x = -1; an easier way to explain this is to set both factors to zero then solve for x. (x+1 = 0).
Another example is: x2 +5x + 6.
Factors of the c-value: 1,2, 3, 6
Factors of the a-value: 1
Mess around with the multiplication and you'll get 2x1 = 2 and 3x1=3. Sum of both products is 3 + 2 = 5 (which is the b-value). Set both factors to zero: x +2 = 0. x+3 = 0. The solutions are: -3,-2. (or x = -2,-3)
Hope this helps!