Description for Correct answer:
Given equation is

\( \Large 2x^{2}+12x+18=0 \)

= \( \Large x^{2}+6x+9=0 \) [divide by 2]

= \( \Large x^{2}+3x+3x+9=0 \) [by factorisation method]

= \( \Large x \left(x+3\right)+3 \left(x+3\right)=0 \)

= \( \Large \left(x+3\right) \left(x+3\right)=0 \)

= \( \Large \left(x+3\right)^{2}=0 \)

= x+3 = 0

= x = -3