Math HW help? Please Explain how its done?

Question

Factor 2x^2+5x-3.

Answer 1

The equation is 2x² + 5x - 3 = 0.

Separate variables and constants aside by adding 3 each side

2x² + 5x = 3

Here x² coefficient is 2, for perfect square make x² coefficient 1.

Divide each side by 2.

x² + 5/2x = 3/2

To change the expression into a perfect square trinomial add (half the x coefficient) ² to each side of the expression

Here x coefficient = 5/2. so, (half the x coefficient) ² = (5/4)²=25/16

Add 25/4 to each side.

x² + 5/2x + 25/4= 3/2 + 25/16

(x + 5/4)²= 24/16 + 25/ 16 = 49 /16

Take square root both sides 

x + 5/4= √49/16

x = -5/4 ± 7/4

x = -5/4- 7/4 and    x = -5/4 + 7/4

x = -12/4 and x = 2/4

x = -3 or 1/2 .

Answer 2

Given that

Take common (x + 3)

(x + 3) (2 x - 1)