How do you solve #-6n-10=-2n+4(1-3n)#?

This might look a little intimidating, but the process is fairly straightforward.
To begin, let's distribute the #4#, so that the problem becomes #-6n-10=-2n+4-12n#.
From here, we should combine like-terms. That leaves us with
#-6n-10=-14n+4#.

We need to isolate the variable, so our next step should be to move all the constants to one side and all the variables to the other.

#-6n-10=-14n+4#
#color(green)(+14n)color(white)()color(purple)(+10)=color(green)(+14n)color(white)(.)color(purple)(+10)#

Now we have #8n=14#, and if we divide by #8# on both sides we have #n=14/8# or #1.75#.

The first step is to distribute the bracket.

#rArr-6n-10=-2n+4-12n#

#rArr-6n-10=-14n+4#

Collect terms in n on the left side and numeric values on the right side.

add 14n to both sides.

#-6n+14n-10=cancel(-14n)cancel(+14n)+4#

#rArr8n-10=4#

add 10 to both sides.

#8ncancel(-10)cancel(+10)=4+10#

#rArr8n=14#

divide both sides by 8

#(cancel(8) n)/cancel(8)=14/8#

#rArrn=14/8=7/4#

#color(blue)"As a check"#

Substitute this value into the equation and if the left side equals the right side then it is the solution.

#"left side "=(-6xx7/4)-10=-21/2-10=-41/2#

#"right side "=(-2xx7/4)+4(1-3xx7/4)#

#color(white)(right sidexx)=-7/2+4(1-21/4)#

#color(white)(right sidexx)=-7/2-17=-41/2#

#rArrn=7/4" is the solution"#