2x^2=x+6

Solving quadratics by factoring

x = - 3/2 or + 2

Step-by-step explanation:

Write in standard form:

2x^2 - x - 6 = 0

Find factors of 2 (-6), the product of the first and last coefficients, that have a sum of - 1, the middle coefficient.

-12 = - 4·3

Split the middle term using those factors:

2x^2 - 4x + 3x - 6 = 0

Factor the pairs of terms:

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

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

Use the zero product rule to identify solutions.

2x + 3 = 0 ⇒ x = - 3/2

x - 2 = 0 ⇒ x = 2