$$ -3 x^{2}+42 x-135=0 $$ [Hint: Divide by -3 first] $$ x=1 $$

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1. Start with the equation
   $$
   -3x^2 + 42x - 135 = 0.
   $$

2. Divide the entire equation by $$-3$$ to simplify:
   $$
   x^2 - 14x + 45 = 0.
   $$

3. Factor the quadratic. We need two numbers that multiply to $$45$$ and add to $$-14$$. These numbers are $$-5$$ and $$-9$$, since
   $$
   -5 \cdot (-9) = 45 \quad \text{and} \quad -5 + (-9) = -14.
   $$

4. Write the factored form:
   $$
   (x - 5)(x - 9) = 0.
   $$

5. Solve each factor:
   $$
   x - 5 = 0 \quad \Rightarrow \quad x = 5,
   $$
   $$
   x - 9 = 0 \quad \Rightarrow \quad x = 9.
   $$

The solutions to the equation are $$x = 5$$ and $$x = 9$$.
The solutions are $$x = 5$$ and $$x = 9$$.

\( -3 x^{2}+42 x-135=0 \) [Hint: Divide by -3 first] \( x=1 \)

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