Question 293099
{{{(3v-2)(2v+1)=3v^2-11v-10}}} Start with the given equation.



{{{6v^2-v-2=3v^2-11v-10}}} FOIL



{{{6v^2-v-2-3v^2+11v+10=0}}} Get every term to the left side.



{{{3v^2+10v+8=0}}} Combine like terms.



Notice that the quadratic {{{3v^2+10v+8}}} is in the form of {{{Av^2+Bv+C}}} where {{{A=3}}}, {{{B=10}}}, and {{{C=8}}}



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



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



{{{v = (-(10) +- sqrt( (10)^2-4(3)(8) ))/(2(3))}}} Plug in  {{{A=3}}}, {{{B=10}}}, and {{{C=8}}}



{{{v = (-10 +- sqrt( 100-4(3)(8) ))/(2(3))}}} Square {{{10}}} to get {{{100}}}. 



{{{v = (-10 +- sqrt( 100-96 ))/(2(3))}}} Multiply {{{4(3)(8)}}} to get {{{96}}}



{{{v = (-10 +- sqrt( 4 ))/(2(3))}}} Subtract {{{96}}} from {{{100}}} to get {{{4}}}



{{{v = (-10 +- sqrt( 4 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{v = (-10 +- 2)/(6)}}} Take the square root of {{{4}}} to get {{{2}}}. 



{{{v = (-10 + 2)/(6)}}} or {{{v = (-10 - 2)/(6)}}} Break up the expression. 



{{{v = (-8)/(6)}}} or {{{v =  (-12)/(6)}}} Combine like terms. 



{{{v = -4/3}}} or {{{v = -2}}} Simplify. 



So the solutions are {{{v = -4/3}}} or {{{v = -2}}}