分解因式:(x*x+4*x)(x*x+4*x+7)+12

(x^2+4x)(x^2+4x+7)+12
=(x^2+4x)^2+7(x^2+4x)+12
=[(x^2+4x)+3][(x^2+4x)+4]
=(x^2+4x+3)(x^2+4x+4)
=(x+3)(x+1)(x+2)^2

Let y=(x*x + 4*x)

(x*x+4*x)(x*x+4*x+7)+12
= y ( y + 7 ) +12
= y*y + 7*y +12
= (y+3) (y+4)

=> y = -3 or y = -4
=> x*x + 4*x = -3 or x*x+4*x = -4
=> x*x + 4*x +3=0 or x*x + 4*x + 4 =0

接下來用公式 [ -b +- sqrt(b^2-4ac) ] /2分別代入兩條算式找答案