Question 215001
{{{3(x-6)^2+x^2=x(x+72)-48x}}} Start with the given equation.



{{{3(x^2-12x+36)+x^2=x(x+72)-48x}}} FOIL



{{{3x^2-36x+108+x^2=x^2+72x-48x}}} Distribute



{{{3x^2-36x+108+x^2-1x^2-72x+48x=0}}} Get every term to the left side.



{{{3x^2-60x+108=0}}} Combine like terms.



Notice that the quadratic {{{3x^2-60x+108}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=3}}}, {{{B=-60}}}, and {{{C=108}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(-60) +- sqrt( (-60)^2-4(3)(108) ))/(2(3))}}} Plug in  {{{A=3}}}, {{{B=-60}}}, and {{{C=108}}}



{{{x = (60 +- sqrt( (-60)^2-4(3)(108) ))/(2(3))}}} Negate {{{-60}}} to get {{{60}}}. 



{{{x = (60 +- sqrt( 3600-4(3)(108) ))/(2(3))}}} Square {{{-60}}} to get {{{3600}}}. 



{{{x = (60 +- sqrt( 3600-1296 ))/(2(3))}}} Multiply {{{4(3)(108)}}} to get {{{1296}}}



{{{x = (60 +- sqrt( 2304 ))/(2(3))}}} Subtract {{{1296}}} from {{{3600}}} to get {{{2304}}}



{{{x = (60 +- sqrt( 2304 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (60 +- 48)/(6)}}} Take the square root of {{{2304}}} to get {{{48}}}. 



{{{x = (60 + 48)/(6)}}} or {{{x = (60 - 48)/(6)}}} Break up the expression. 



{{{x = (108)/(6)}}} or {{{x =  (12)/(6)}}} Combine like terms. 



{{{x = 18}}} or {{{x = 2}}} Simplify. 



So the solutions are {{{x = 18}}} or {{{x = 2}}}