To solve the equation \( 900:(210 + x) = 36 \), we can rewrite it in a clearer form. The colon (:) represents division, so we can rewrite the equation as:
\[ \frac{900}{210 + x} = 36 \]
Now, to eliminate the fraction, we can multiply both sides of the equation by \( 210 + x \):
\[ 900 = 36(210 + x) \]
Next, distribute the 36 on the right side:
\[ 900 = 36 \cdot 210 + 36x \]
Calculating \( 36 \cdot 210 \):
\[ 36 \cdot 210 = 7560 \]
So the equation becomes:
\[ 900 = 7560 + 36x \]
Now, we can isolate the term with \( x \) by subtracting 7560 from both sides:
\[ 900 - 7560 = 36x \]
\[ -6660 = 36x \]
Next, divide both sides by 36 to solve for \( x \):
\[ x = \frac{-6660}{36} \]
Calculating \( \frac{-6660}{36} \):
\[ x = -185 \]
Therefore, the solution is:
\[ \boxed{-185} \]