Question 149479
{{{3x (3x + 4) = -4}}} Start with the given equation.



{{{9x^2 + 12x= -4}}} Distribute.


{{{9x^2+12x+4=0}}} Get all terms to the left side.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=9}}}, {{{b=12}}}, and {{{c=4}}}



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(9)(4) ))/(2(9))}}} Plug in  {{{a=9}}}, {{{b=12}}}, and {{{c=4}}}



{{{x = (-12 +- sqrt( 144-4(9)(4) ))/(2(9))}}} Square {{{12}}} to get {{{144}}}. 



{{{x = (-12 +- sqrt( 144-144 ))/(2(9))}}} Multiply {{{4(9)(4)}}} to get {{{144}}}



{{{x = (-12 +- sqrt( 0 ))/(2(9))}}} Subtract {{{144}}} from {{{144}}} to get {{{0}}}



{{{x = (-12 +- sqrt( 0 ))/(18)}}} Multiply {{{2}}} and {{{9}}} to get {{{18}}}. 



{{{x = (-12 +- 0)/(18)}}} Take the square root of {{{0}}} to get {{{0}}}. 



{{{x = (-12 + 0)/(18)}}} or {{{x = (-12 - 0)/(18)}}} Break up the expression. 



{{{x = (-12)/(18)}}} or {{{x =  (-12)/(18)}}} Combine like terms. 



{{{x = -2/3}}} or {{{x = -2/3}}} Simplify.



So the answer is {{{x = -2/3}}} (with a multiplicity of 2).