Step By Step for factoring this equation? 2x^2+x-3=0

Question

Step By Step for factoring this equation?

`2x^2+x-3=0`

Answer 1

x = -
`(3)/(2)` , x = 1

Explanation:

I assume you require the solution to the equation

2x² + x - 3 = 0 ← in standard form

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

product = 2 × - 3 = - 6 and sum = + 1

the factors are - 2 and + 3

use these factors to split the x- term

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

2x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(2x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ( add 1 to each side )

x = 1

2x + 3 = 0 ( subtract 3 from each side )

2x = - 3 ( divide each side by 2 )

x = -
`(3)/(2)`

solutions are x = -
`(3)/(2)` , x = 1