Question

(x-1)(x²+8x+16)=6(x+4)

Answer 1

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Answer 2

x²+8x+16=(x+4)²=(x+4)(x+4)

(x-1)(x²+8x+16)=6(x+4)
(x-1)(x+4)(x+4)-6(x+4)=0
(x+4)((x-1)(x+4)-6)=0

(x-1)(x+4)=x²-x+4x-4=x²+3x-4

(x+4)(x²+3x-4-6)=0
(x+4)(x²+3x-10)=0
$left { {{x+4=0} atop { x^{2} +3x-10=0}} right. \ left { {{x=-4} atop { x^{2} +3x-10=0}} right.$

x² +3x-10=0
D=3²-4*(-10)*1=9+0=49=7²
$x_{1}= frac{-3- sqrt{49} }{2*1} = frac{-3-7}{2} = frac{-10}{2}=-5 \ x_{2}= frac{-3+ sqrt{49} }{2*1} = frac{-3+7}{2} = frac{4}{2}=2$

$left { {{x=-4}atop { x=2}} atop { x=-5}}right.$