To solve the equation \(-3x + 3(5x + 2) = 2x + 10x + 9\), we will first simplify both sides.
- Start by distributing the \(3\) on the left side:
\[ -3x + 3(5x) + 3(2) = -3x + 15x + 6 \]
So, the left side simplifies to:
\[ -3x + 15x + 6 = 12x + 6 \]
- Now simplify the right side. Combine like terms:
\[ 2x + 10x + 9 = 12x + 9 \]
- Now we rewrite the equation with the simplified left and right sides:
\[ 12x + 6 = 12x + 9 \]
- Subtract \(12x\) from both sides:
\[ 6 = 9 \]
Since this statement is false (there is no value of \(x\) that can make this true), the original equation has no solutions. The final answer is that there are no solutions to the equation.