To solve the equation \(3x(5x + 2) - 6x - 1 = 5 - 2x + 15x^2\), follow these steps:

1. Distribute and simplify both sides of the equation.
2. Combine like terms.
3. Move all terms to one side to set the equation to zero.
4. Solve the resulting quadratic equation.

Let's go through these steps:

### Step 1: Distribute and simplify both sides
Distribute \(3x\) on the left side:
\[3x(5x + 2) - 6x - 1 = 5 - 2x + 15x^2\]
\[15x^2 + 6x - 6x - 1 = 5 - 2x + 15x^2\]

### Step 2: Combine like terms
Combine the \(6x\) and \(-6x\) on the left side:
\[15x^2 - 1 = 5 - 2x + 15x^2\]

### Step 3: Move all terms to one side
Subtract \(15x^2\) from both sides:
\[15x^2 - 1 - 15x^2 = 5 - 2x + 15x^2 - 15x^2\]
\[-1 = 5 - 2x\]

### Step 4: Solve the resulting linear equation
Add \(2x\) to both sides:
\[-1 + 2x = 5\]
\[2x = 6\]

Divide by 2:
\[x = 3\]

So, the solution to the equation \(3x(5x + 2) - 6x - 1 = 5 - 2x + 15x^2\) is:
\[x = 3\]