To solve the equation \(2^{(x+3)} + 2^x = 36\), we can start by simplifying the expression. Notice that \(2^{(x+3)}\) can be rewritten using the properties of exponents:

\[2^{(x+3)} = 2^x \cdot 2^3 = 2^x \cdot 8\]

So the equation becomes:

\[8 \cdot 2^x + 2^x = 36\]

Factor out \(2^x\) from the left side:

\[2^x (8 + 1) = 36\]

Simplify inside the parentheses:

\[2^x \cdot 9 = 36\]

Divide both sides by 9:

\[2^x = \frac{36}{9}\]

\[2^x = 4\]

Since \(4\) can be written as \(2^2\), we have:

\[2^x = 2^2\]

Therefore, the exponents must be equal:

\[x = 2\]

So, the solution to the equation \(2^{(x+3)} + 2^x = 36\) is:

\[x = 2\]