Question 104756
Look for a solution 
{{{x^2 + 7x – 30=(x+a)(x+b)}}}
When the equation is expanded with a,b,
{{{(x+a)(x+b)=x^2+(a+b)x+ab}}}
Compare that to your equation and you find that,  
{{{a+b=7}}}
{{{ab=-30}}}
Look for integer factors (a,b) of 30
(1,30)
(2,15)
(3,10)
(5,6)
Factors (3,10) look promising since their difference is 7. 
Now to get the signs right. 
The smaller number needs to be negative for the sum to positive. 
(a,b)=(-3,10)
{{{a+b=7}}}
{{{a*b=-30}}}
{{{x^2+7x-30=(x+a)(x+b)}}}
{{{x^2+7x-30=(x+(-3))(x+10)}}}
{{{x^2+7x-30=(x-3)(x+10)}}}