solve 4tan^2x+5tanx=6

Question

campbell_st · Answer

well this is a quadratic equation 

$$4\tan^2(x) + 5(x) - 6 = 0$$

mathstudent55 · Answer

Bring the 6 over to the left side.
Then solve the quadratic equation for tan x.
Then solve the trig part.

campbell_st · Answer

it can be factored.... 

to 

(4tan(x) + 8)(4tan(x) - 3)
-----------------------  = 0
                4

remove a common factor from the 1st binomial 

4(tan(x) + 2)(4tan(x) - 3) 
----------------------    = 0
                4

cancel the common factor then solve for x

anonymous · Answer

wait can you reexplain it to me please... I don't understand how you factored it

campbell_st · Answer

ok... well a simple method for factoring non-monic quadratic is multiply a and c

$$ax^2 + bx + c=0$$
so in your question it was 

4 x - 6 = -24

now find the factors that add to b, or in your question 5.......8 and - 3

then you write 

(ax + factor 1)(ax + factor 2)
-------------------------    =0
                   a  

and you'll find that there are common factors in the binomial that 
cancel with the denominator... 

it works everytime

anonymous · Answer

oh okay...thank you so much