Question 687953
The first step in solving for x in this equation, is to expand the factoring on the left side of the equation:


(2x + 1)(x + 5) =


{{{2x*x + 2x*5 + 1x + 1*5}}} =


{{{2x^2 + 10x + 1x + 5}}} =


{{{2x^2 + 11x + 5}}}


Next we want to set this equation equal to 0.  To do this, add 3 to both sides, giving us


{{{2x^2 + 11x + 8 = 0}}}


Now, we have a quadratic equation.  Because this equation cannot be factored, we will use the quadratic formula to solve for x.


The quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


In our equation, a = 2, b = 11, and c = 8.  We will plug these numbers into the quadratic formula:


{{{(-11 +- sqrt(11^2 - 4(2)(8)))/(2(2))}}} =


{{{(-11 +- sqrt(121 - 64))/4}}} =


{{{(-11 +- sqrt(57))/4}}}


Final Answer:


x = {{{(-11 + sqrt(57))/4}}},{{{(-11 - sqrt(57))/4}}}