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Question
Solve the following equation by factorization
3(y2 – 6) = y(y + 7) – 3
Solution
3(y2 – 6) = y(y + 7) – 3
⇒ 3(y2 - 6) = y2 + 7y - 3
⇒ 3y2 - 18 = y2 + 7y - 3
⇒ 3y2 - y2 - 7y - 18 + 3 = 0
⇒ 2y2 - 7y - 15 = 0
⇒ 2y2 - 10y + 3y - 15 = 0
2y(y - 5) + 3(y - 5) = 0
⇒ (y - 5) (2y + 3) = 0
Either y - 5 = 0,
then y = 5
or
2y + 3 = 0,
then 2y = -3
⇒ y = `(-3)/(2)`
Hence y = `(-3)/(2)`, 5.
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