To determine how many solutions the equation \(-15r + 12 = 3(-5r + 4)\) has, we'll start by simplifying both sides of the equation.
First, expand the right-hand side:
\[ 3(-5r + 4) = 3 \cdot -5r + 3 \cdot 4 = -15r + 12 \]
Now, the equation can be rewritten as:
\[ -15r + 12 = -15r + 12 \]
Since both sides of the equation are identical, this means that the equation is true for all values of \(r\).
Therefore, there are infinitely many solutions to this equation.