Question

how do I solve this 8(c-9)=6(2c-12)-4c

Answer 1

$8(c-9)=6(2c-12)-4c\\\\ 8c-72=12c-72-4c\\\\ 8c-72=8c-72\\\\0=0\\\\There\ are\ infinitely\ many\ solutions.$

Answer 2

8(c-9) = 6(2c-12)-4c

Okay let us solve it together.
Multiply out and expand the brackets.

8*c -8*9 = 6*2c -6*12 -4c
8c -72    = 12c -72 -4c      Re arrange by taking the cs to one side
8c -12c +4c = -72 + 72
0 = 0

For this kind of statement it means C can be any number, and it would satisfy the equation.
Cheers.