Question

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

Answer 1

$x(x-6)=4(x+6)\ \ \ |use\ distributive\ property\ a(b+c)=ab+ac\\\\x(x)+x(-6)=4(x)+4(6)\\\\x^2-6x=4x+24\ \ \ \ |subtract\ 4x\ and\ 24\ from\ both\ sides\\\\x^2-10x-24=0\\\\x^2-12x+2x-24=0\\\\x(x-12)+2(x-12)=0\iff(x-12)(x+2)=0\\\\therefore\\\\x-12=0\ or\ x+2=0\\\\Answer:\boxed{x=12\ or\ x=-2}$

Answer 2

        x(x - 6) = 4(x + 6)
    x(x) - x(6) = 4(x) + 4(6)
         x² - 6x = 4x + 24
             - 4x  - 4x        
       x² - 10x = 24
x² - 10x - 24 = 24 - 24
x² - 10x - 24 = 0
x = -(-10) +/- √((-10) - 4(1)(-24))
                         2(1)
x = 10 +/- √(100 + 96)
                   2
x = 10 +/- √(196)
                2
x = 10 +/- 14
            2
x = 5 + 7
x = 5 + 7    U    x = 5 - 7
x = 12               x = -2
The values of x in the equation is either equal to 12 or -2.