1. **State the problem:** Solve the equation $9 = 12x - 3x^2$ by factoring. 2. **Rewrite the equation in standard form:** Move all terms to one side: $$9 - 12x + 3x^2 = 0$$ which is equivalent to $$3x^2 - 12x + 9 = 0$$ 3. **Factor out the greatest common factor (GCF):** $$3(x^2 - 4x + 3) = 0$$ 4. **Factor the quadratic inside the parentheses:** We look for two numbers that multiply to $3$ and add to $-4$, which are $-3$ and $-1$. $$3(x - 3)(x - 1) = 0$$ 5. **Set each factor equal to zero and solve:** $$x - 3 = 0 \Rightarrow x = 3$$ $$x - 1 = 0 \Rightarrow x = 1$$ 6. **Final answer:** $$x = 1 \text{ or } x = 3$$ \n 3. **State the problem:** Solve the equation $-96 = -8v - 8v^2$ by factoring. 2. **Rewrite the equation in standard form:** Move all terms to one side: $$-96 + 8v + 8v^2 = 0$$ which is equivalent to $$8v^2 + 8v - 96 = 0$$ 3. **Factor out the GCF:** $$8(v^2 + v - 12) = 0$$ 4. **Factor the quadratic inside the parentheses:** We look for two numbers that multiply to $-12$ and add to $1$, which are $4$ and $-3$. $$8(v + 4)(v - 3) = 0$$ 5. **Set each factor equal to zero and solve:** $$v + 4 = 0 \Rightarrow v = -4$$ $$v - 3 = 0 \Rightarrow v = 3$$ 6. **Final answer:** $$v = -4 \text{ or } v = 3$$ \n 5. **State the problem:** Solve the equation $r^2 + 14 = -9r$ by factoring. 2. **Rewrite the equation in standard form:** Move all terms to one side: $$r^2 + 9r + 14 = 0$$ 3. **Factor the quadratic:** We look for two numbers that multiply to $14$ and add to $9$, which are $7$ and $2$. $$ (r + 7)(r + 2) = 0$$ 4. **Set each factor equal to zero and solve:** $$r + 7 = 0 \Rightarrow r = -7$$ $$r + 2 = 0 \Rightarrow r = -2$$ 5. **Final answer:** $$r = -7 \text{ or } r = -2$$