Question

(c-30)(c-120)=184 how do I solve it

Answer 1

$(c-30)(c-120)=184\ \ \ \ | multiply \ both\ brackets\\\\ c^2-120c-30c+3600=184\ \ \ \ | subtract\ 184\\\\ c^2-150c+3416=\ \ \ \ | factorisation\\\\c^2-122c-28c+3416 \\\\(c-122)(c-28)=0\\\\c=122\ \ or\ \ \ c=28$

Answer 2

$(c-30)(c-120)=184\\ c^2-120c-30c+3600=184\\ c^2-150c+3416=0\\ c^2-150c+5625-2209=0\\ (c-75)^2=2209\\ c-75=\sqrt{2209} \vee c-75=-\sqrt{2209}\\ c=75+47 \vee c=75-47\\ c=122 \vee c=28$