please help me understand the process of doing these questions, Thanks!

x^2+10x=-21

get all on one side

x^2+10x+21=0

factor-what plus what =10

           these two numbers also must multiply to 21

7+3=10

7*3=21

(x+7)(x+3)=0

x+7=0 or x+3=0

x=-7 or x=-3

x^2+10x=-21

Step 1: Add 21 to both sides to make the equation equal to 0

x^2+10x+21= 0

Step 2 : Use Factoring to find the zeroes of the equation

(x+3)(x+7) = Factored Answer

Step 3: Make each part equal to =zero to find the zeroes

x+3= 0        x+7= 0

x=-3             x= -7