Question

How do i solve this? (by factoring) x(x+3)=x+8

Answer 1

$\sf x\left(x+3\right)=x+8\\\\\\\\x^2+3x=x+8\\\\\\\\\sf \boxed{\sf\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}}\\\\\\\\\sf x^2+3x-8=x+8-8\\\\\\\\\sf \boxed{\sf \mathrm{Simplify}}\\\\\\\\\sf x^2+3x-8=x\\\\\\\\\boxed{\sf \mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}}\\\\\\\\\sf x^2+3x-8-x=x-x\\\\\\\\\boxed{\sf \mathrm{Simplify}}\\\\\\\\\sf x^2+2x-8=0\\\\\\\\\boxed{\sf factor~ x^2+2x-8=0}\\\\\\\\\sf \left(x-2\right)\left(x+4\right)=0$

$\sf \boxed{\sf \mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0}\\\\\\\\\sf x-2=0\quad \mathrm{or}\quad \:x+4=0\\\\\\\\\boxed{\sf \{x=2\}}\\\\\boxed{\sf \{x=-4 \} }$