Need help solving: x(2x+7)=0 & 9x squared + 12x +14 (the answer is a fraction)I do not understand factoring the quadratic equation when the...

We'll solve the first
equation:

x(2x+7) = 0

The
product is cancelling if one of the factors is
cancelling.

We'll cancel out the first factor,
x:

x = 0

We'll cancel out the
next factor, x:

2x+  7 = 0

2x
= -7 =>> x = -7/2

We'll solve the second
equation

9x^2 + 12x + 14 =
0

We'll apply quadratic formula to determine it's
roots::

x1 =
[-b+sqrt(b^2-4ac)]/2a

We'll identify he coefficients
a,b,c.

a = 9, b = 12 and c =
14

x1 = [-12+sqrt(144 -
504)]/18

x1 =
[-12+sqrt(-360)]/18

x1 =
(-12+6i*sqrt10)/18

We'll divide by
6:

x1 = (-2+i*sqrt10)/3

x2 =
(-2-i*sqrt10)/3

The real roots of the 1st
equation are x = 0 and x = -7/2 and the roots of the 2nd equation are complex number and
they are x1 = (-2+i*sqrt10)/3 and x2 =
(-2-i*sqrt10)/3.