Given: [tex]x^2 + 6x + 2x + 12 = 0.[/tex]
1. Combining like terms (here terms 6x and 2x both contain x, then we can combine them):
[tex]x^2+(6x+2x)+12=0,\\\\x^2+8x+12=0.[/tex]
2. Distributive postulate:
[tex]x^2+8x+12=(x+6)(x+2).[/tex]
The equation is
[tex](x+6)(x+2)=0.[/tex]
3. Zero product postulate (zero product postulate state that if a product of two factors is equal to zero, then first factor is equal to zero or second factor is equal to zero):
[tex]x+6=0 \text{ or } x+2=0.[/tex]
4. Subtraction property of equality:
a) subtract 6 from the first equation:
[tex]x+6=0\Rightarrow x+6-6=-6, \ x=-6.[/tex]
b) subtract 2 from the second equation:
[tex]x+2=0\Rightarrow x+2-2=-2, \ x=-2.[/tex]
