Can't Solve 4x+3*2x+2+32=0? Get Help Here!

[1/2"]

Homework Statement

The problem is 4 ^x+ 3*2 ^x+2 + 32 = 0

Homework Equations

None

The Attempt at a Solution

I can’t get to any solution in this problem but I have come to a point (if it is nearing any solution though) but I am not sure whether it is correct or not.
Well what I have done is
2 ^2x + (2+1)2 ^x+2 + 2 ⁵=0
==> 2 ^2x + 2*2 ^x+2 + 2 ^x+2 +2 ⁵=0
==>2 ^2x + 2 ^x+3 + 2 ^x+2 +2 ⁵=0
( That’s all I have done)
I would be very thankful to receive any help!
Thank you!

 

[Mark44]

4^x = (2²)^x = 2^2x and 2^{x + 2} = 2²* 2^x

Your equation can be rewritten so that it is quadratic in form.

 

[1/2"]

4^x = (2²)^x = 2^2x and 2^{x + 2} = 2²* 2^x

Your equation can be rewritten so that it is quadratic in form.

Ok so I write it like this
2 ^2x + 2 ^x*2 ³ + 2 ^x *2 ² +2 ⁵=0
But where does it go after this??

 

[annoymage]

you see, that 2^x is the common variable,
so you can solve it like solving quadratic equation..

or if you wan to see it more clearly, try let u = 2^x

 

[Mark44]

Ok so I write it like this
2 ^2x + 2 ^x*2 ³ + 2 ^x *2 ² +2 ⁵=0
But where does it go after this??

your coefficient of 2^x is wrong. There should be only a single 2^x term, not two of them as you show. 3*2^x+2 does NOT expand to a sum of two terms.

Also, rewriting 32 as 2⁵ does you no good.