Solve the following equation by factorization: 5(3x + 1)2 + 6(3x + 1) - 8 = 0

Let us consider y = 3x + 1. Substituting y = 3x + 1 in equation 5(3x + 1)2 + 6(3x + 1) - 8 = 0, we get : ⇒ 5y2 + 6y - 8 = 0 ⇒ 5y2 + 10y - 4y - 8 = 0 ⇒ 5y(y + 2) - 4(y + 2) = 0 ⇒ (5y - 4)(y + 2) = 0 ⇒ (5y - 4) = 0 or (y + 2) = 0 [Using Zero-product rule] ⇒ 5y = 4 or y = -2 ⇒ y = or y = -2. Now we have, Case 1 : y = Case 2 : y = -2 ⇒ y = -2 ⇒ 3x + 1 = -2 ⇒ 3x = -2 - 1 ⇒ 3x = -3 ⇒ x = ⇒ x = -1. Hence, x = .

Mathematics

Solve the following equation by factorization:
5(3x + 1)² + 6(3x + 1) - 8 = 0

Quadratic Equations

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Mathematics

Solve the following equation by factorization:5(3x + 1)2 + 6(3x + 1) - 8 = 0

Quadratic Equations

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Solve the following equation by factorization:
5(3x + 1)² + 6(3x + 1) - 8 = 0