Question 211462
{{{(x-3)(x-2)=(x+5)(2x-3)+21}}} Start with the given equation.



{{{x^2-5x+6=2x^2+7x-15+21}}} FOIL



{{{x^2-5x+6=2x^2+7x+6}}} Combine like terms.



{{{x^2-5x+6-2x^2-7x-6=0}}} Get every term to the left side.



{{{-x^2-12x=0}}} Combine like terms.



Notice that the quadratic {{{-x^2-12x+0}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=-1}}}, {{{B=-12}}}, and {{{C=0}}}



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



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



{{{x = (-(-12) +- sqrt( (-12)^2-4(-1)(0) ))/(2(-1))}}} Plug in  {{{A=-1}}}, {{{B=-12}}}, and {{{C=0}}}



{{{x = (12 +- sqrt( (-12)^2-4(-1)(0) ))/(2(-1))}}} Negate {{{-12}}} to get {{{12}}}. 



{{{x = (12 +- sqrt( 144-4(-1)(0) ))/(2(-1))}}} Square {{{-12}}} to get {{{144}}}. 



{{{x = (12 +- sqrt( 144-0 ))/(2(-1))}}} Multiply {{{4(-1)(0)}}} to get {{{0}}}



{{{x = (12 +- sqrt( 144 ))/(2(-1))}}} Subtract {{{0}}} from {{{144}}} to get {{{144}}}



{{{x = (12 +- sqrt( 144 ))/(-2)}}} Multiply {{{2}}} and {{{-1}}} to get {{{-2}}}. 



{{{x = (12 +- 12)/(-2)}}} Take the square root of {{{144}}} to get {{{12}}}. 



{{{x = (12 + 12)/(-2)}}} or {{{x = (12 - 12)/(-2)}}} Break up the expression. 



{{{x = (24)/(-2)}}} or {{{x =  (0)/(-2)}}} Combine like terms. 



{{{x = -12}}} or {{{x = 0}}} Simplify. 



So the solutions are {{{x = -12}}} or {{{x = 0}}}