To solve the equation \(2x - 5 = 3(4x + 5)\), we will follow these steps:
Step 1: Distribute the right side of the equation
First, we need to distribute the \(3\) on the right-hand side:
\[ 3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15 \]
So, the equation now looks like:
\[ 2x - 5 = 12x + 15 \]
Step 2: Move all terms involving \(x\) to one side
We can move \(12x\) to the left-hand side by subtracting \(12x\) from both sides:
\[ 2x - 12x - 5 = 15 \]
This simplifies to:
\[ -10x - 5 = 15 \]
Step 3: Move constant terms to the other side
Next, we want to isolate the terms with \(x\). We can do this by adding \(5\) to both sides:
\[ -10x - 5 + 5 = 15 + 5 \]
This simplifies to:
\[ -10x = 20 \]
Step 4: Solve for \(x\)
Now we will divide both sides by \(-10\):
\[ x = \frac{20}{-10} \]
This simplifies to:
\[ x = -2 \]
Final Solution
The solution to the equation \(2x - 5 = 3(4x + 5)\) is:
\[ \boxed{-2} \]