2^x-10*(2^-x)+3

Question

Solve for x in this exponetial equation. I know the answer is 1 but I don't know the steps

Answer 1

This can be written (2²ˣ-10+3×2ˣ)/2ˣ or (2²ˣ+3×2ˣ-10)/2ˣ=(2ˣ+5)(2ˣ-2)/2ˣ.

If this expression is to be equal to zero, then 2ˣ=2 so x=1.

CHECK: 2-10/2+3=2-5+3=0.