Verified answer

a.

You can not solve this as it is not an equation without an =, unless it is supposed to be '= 0', which is what I am assuming in this:

4x^2 + 12x = 0

4x(x + 3) = 0

4x = 0

x = 0

x + 3 = 0

x = -3

x = [-3, 0]

b.

f(x) = 4x^2 + 12x + c

f(0) = 4(0)^2 + 12(0) + c

f(0) = c

4x^2 + 12x + c = 0

ax^2 + bx + c = 0

a = 4

b = 12

c = ?

b = 2 * sqrt(ac)

b / 2 = sqrt(ac)

(b / 2)^2 = ac

(b / 2)^2 / a = c

(12 / 2)^2 / 4 = c

6^2 / 4 = c

36 / 4 = c

c = 9

4x^2 + 12x + 9 = 0

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

(2x + 3)^2 = 0