Content Request: Find the length of each side of a new square

I had great difficulty in "seeing" the equation to solve the below word problem, and I did not want to just be given the equation. After much time of trail and error, mostly error, I was able figure it out. Why this equation was so difficult for me "to see", don't know? But to help me remember this equation, and maybe to help others, I'm posting here.

Question:

When each side of a new square is increased by 3 inches, the area is increased be 51 square inches.
Find the length of each side of the new square.

Solution;

(x + 3)^2 = x^2 + 51,

(x + 3)(x + 3) = x^2 + 51,
x^2 + 6x + 9 = x^2 + 51,
x^2 - x^2 + 6x = 51 - 9,
6x = 42
x = 7,   (7 + 3) = 10" new length for each side of the increased square.

Not a solution, however, for some reason "my mind" was "fixated" on the below. Is this common?

2(x + 3) = 2x + 51

which of course, is not the solution.

Would Khan Academy consider creating a couple of videos on this and similar scenarios, please?