Question

what are the values of x in the equation x(x+6)=4(x+6)

Answer 1

Since both sides has same factor (x+6), we can set (x+6) equal to 0.

So we would have one of solution x = -6. (because this would have us x·0 = 4·0 )

Now when x is NOT equal to -6, we can divide both sides by (x+6), leaving us 

x = 4

So answer is x = -6 or 4.

Answer 2

       x(x + 6) = 4(x + 6)
   x(x) + x(6) = 4(x) + 4(6)
       x² + 6x = 4x + 24
            - 4x  - 4x       
       x² + 2x = 24
x² + 2x - 24 = 24 - 24
 x² + 2x - 24 = 0
x = -(2) ± √((2)² - 4(1)(-24))
                       2(1)
x = -2 ± √(4 + 96)
               2
x = -2 ± √(100)
             2
x = -2 ± 10
          2
x = -1 ± 5
x = -1 + 5    U    x = -1 - 5
x = 4    U    x = -6