Solve the equation by factoring 2x^2+x-6=0

x = - 2, x =

Step-by-step explanation:

Given

2x² + x - 6 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 6 = - 12 and sum = + 1

The factors are + 4 and - 3

Use these factors to split the x- term

2x² + 4x - 3x - 6 = 0 ( factor the firs/second and third/fourth terms )

2x(x + 2) - 3(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x - 3 = 0 ⇒ 2x = 3 ⇒ x =

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