First lets simplify the equation a little:
#5tan(2x-40)=6-1=5#
#tan(2x-40)=5/5 =1#
Now, the definition of the tangent is #sin x/cos x# so we know that a division only comes out to 1 when the numerator and the denominator are equal.
#sin# and #cos# are only equal at 4 values between 0 and 360, which are 45, 135, 225 and 315, leaving us with 4 equations to solve for x:
#2x-40=45#
#2x-40=135#
#2x-40=225#
#2x-40=315#
Giving us the 4 results:
#2x=45+40=85#, so: #x=85/2=42.5#
#2x=135+40=175#, so: #x=175/2=87.5#
#2x=225+40=265#, so: #x=265/2=132.5#
#2x=315+40=355#, so: #x=355/2=177.5#
