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13 votes
13 votes
Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12.

User Dan Nestor
by
2.8k points

2 Answers

15 votes
15 votes

Answer: Sol={-6,1}

Explanation:

1) we are searching value of x in R


(x+2)(x+3)=12\\x^2+2x+3x+6-12=0\\x^2+5x-6=0\\\\x^2-x+6x-6=0\\\\x(x-1)+6(x-1)=0\\\\(x-1)(x+6)=0\\\\x=1\ or\ x=-6\\Sol=\{-6,1\}\\

2) we are searching value of x in Z.

12=1*12 =(-1)*(-12)

12=2*6=(-2)*(-6)

12=3*4=(-3)*(-4)


\begin{array}cx=&x+2=&x+3=&(x+2)(x+3)=&is\ solution\\---&---&---&---&---\\1&3&4&12&True\\2&4&5&20&False\\3&5&6&30&False\\4&6&7&42&False\\6&8&9&72&False\\12&14&15&210&False\\---&---&---&---&---\\-1&1&0&0&False\\-2&0&1&0&False\\-3&1&2&2&False\\-4&2&3&6&False\\-6&-4&-3&12&True\\-12&-10&-9&90&False\\---&---&---&---&---\\\end{array}\\\\\\\boxed{Sol=\{-6,1\}}

User Mark Wilsdorf
by
2.1k points
20 votes
20 votes

Answer:

Solution

x=1

x=−6

Explanation:

x(+3)+2(x+3)=12

User Muhammad Noman
by
3.3k points