Question 851785
The first step in solving for x, is to multiply each of the terms on the right of the equal sign.  So, let's first multiply 2x + 8 by 4x.  This gives us:


8x^2 + 32x


Now, multiply this result by x, which gives us:


8x^3 + 32x^2


We now have:


8x^3 + 32x^2 = 40


We can make this easier to solve by dividing each term by 8, since each term is divisible by 8.  This gives us:


x^3 + 4x^2 = 5


Next, we can subtract 5 from both sides, giving us:


x^3 + 4x^2 - 5 = 0


Now, since we know that the only possible rational zeros are -1,1,5, or -5 (via the rational zero test), we can test each zero by plugging it into the equation to see if we end up with 0.  If we plug -1,5, and -5 in for x, one at a time, we will not get 0 as our answer.  However, plugging 1 in will give us 0.  So, 1 is one of the values of x.  We can use synthetic division or polynomial long division to divide x^3 + 4x^2 - 5 by x - 1 (because 1 is a value of x as we just discovered, and 1 in factor form is x - 1).  When we divide, we are left with a quotient of:


x^2 + 5x + 5


If we set this equal to zero, we can use the quadratic formula to find our other two values of x:


{{{x = (-5 +- sqrt( 5^2-4*1*5 ))/(2*1) }}} ----->


{{{x = (-5 +- sqrt( 25-20 ))/(2) }}} ----->


{{{x = (-5 +- sqrt( 5 ))/(2) }}}


We now have all of our values of x: {{{1}}}, {{{(-5 + sqrt(5))/(2)}}}, {{{(-5 - sqrt(5))/(2)}}}