Let's rewrite each equation to the standard form $ax^2 + bx + c = 0$, and then identify the coefficients $a$, $b$, and $c$.

1. Original equation: $18x^2 + 9x = 7$

   Standard form: $18x^2 + 9x - 7 = 0$ Coefficients: $a = 18$, $b = 9$, $c = -7$

2. Original equation: $y^2 + 15y = 8y$

   Standard form: $y^2 + 7y = 0$ Coefficients: $a = 1$, $b = 7$, $c = 0$

3. Original equation: $20 - x^2 = x$

   Standard form: $-x^2 - x + 20 = 0$ Coefficients: $a = -1$, $b = -1$, $c = 20$

4. Original equation: $0 = p^2 - 7p$

   Standard form: $p^2 - 7p = 0$ Coefficients: $a = 1$, $b = -7$, $c = 0$

5. Original equation: $m^2 = 16$

   Standard form: $m^2 - 16 = 0$ Coefficients: $a = 1$, $b = 0$, $c = -16$

6. Original equation: $-25t^2 + 4 = 0$

   Standard form: $-25t^2 + 4 = 0$ Coefficients: $a = -25$, $b = 0$, $c = 4$

7. Original equation: $(x+3)^2 = 1$

   Standard form: $x^2 + 6x + 8 = 0$ Coefficients: $a = 1$, $b = 6$, $c = 8$

8. Original equation: $-3a = a^2 + \frac{9}{4}$

   Standard form: $a^2 + 3a + \frac{9}{4} = 0$ Coefficients: $a = 1$, $b = 3$, $c = \frac{9}{4}$

9. Original equation: $n^2 - 4 = 5(n - 3)$

   Standard form: $n^2 - 9n + 11 = 0$ Coefficients: $a = 1$, $b = -9$, $c = 11$

10. Original equation: $5j(j - 3) - 4 = j - 6$

    Standard form: $5j^2 - 16j - 2 = 0$ Coefficients: $a = 5$, $b = -16$, $c = -2$

Would you like more details on any of these transformations or have any questions?

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Here are five related questions:

1. How do you solve quadratic equations after converting them to standard form?
2. Can all quadratic equations be factored easily?
3. What are the methods to find the roots of a quadratic equation?
4. How does the discriminant help in understanding the nature of roots?
5. What are the applications of quadratic equations in real life?

Tip: When converting to standard form, always ensure all terms are on one side of the equation and combined properly before identifying $a$, $b$, and $c$.