# How do you solve #21n ^ { 2} + 5n - 6= 0#?

##### 2 Answers

#### Explanation:

Given:

Now, If :

And If :

Hence Explained.

#### Explanation:

#"factorise the quadratic using the a-c method"#

#"that is factors of "21xx-6=-126" which sum to "+5#

#"the factors of "-126" which sum to + 5 are + 14 and - 9"#

#color(blue)"split the middle term using these factors"#

#rArr21n^2+14n-9n-6=0larrcolor(blue)"factor by grouping"#

#rArrcolor(red)(7n)(3n+2)color(red)(-3)(3n+2)=0#

#"take out the common factor "(3n+2)#

#rArr(3n+2)(color(red)(7n-3))=0#

#"equate each factor to zero and solve for n"#

#3n+2=0rArrn=-2/3#

#7n-3=0rArrn=3/7#