Answer: [tex]\bold{x=\{0,-\dfrac{7}{2}\}}[/tex]
Step-by-step explanation:
[tex](x+2)(2x+3)=6\\\\\text{Expand:}\\2x^2+3x+4x+6=6\\\\\text{Simplify (add like terms):}\\2x^2+7x+6=0\\\\\text{Subtract 6 from both sides:}\\2x^2+7x=0\\\\\text{Factor out the common term:}\\x(2x+7)=0\\\\\text{Apply the Zero Product Property:}\\\boxed{x=0}\qquad 2x+7=0\\\\.\qquad \qquad 2x=-7\\\\.\qquad \qquad \boxed{x=-\dfrac{7}{2}}[/tex]
