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Q: What are the factors of -30a2?

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30a2+89a+63 = (5a+9)(6a+7) when factored

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30a2 + a = 20 ∴ 30a2 + a - 20 = 0 To factor this out, find two values whose sum is equal to the coefficient of the middle term, and whose product is equal to the product of the first and last terms' coefficients: x + y = 1 xy = 600 Because x and y are so close together, we know that they'll be fairly close to the square root of 600, which is about 24.4949. So let's try 24 and 25: 24 × 25 = 600 bingo. So we'll take those two terms, and use them in our original equation, replacing the middle term with each of them (keeping in mind that their sum must equal the middle term): ∴ 30a2 -24a + 25a - 20 = 0 ∴ 6a(5a - 4) + 5(5a - 4) = 0 ∴ (6a + 5)(5a - 4) = 0 ∴ a ∈ {-5/6, 4/5}

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