what is the answer to 4p^2+12p+9=0?

This is in the form:
ax^2 + bx + c = 0

multiiply a * x = (ax)

What two numbers go into (ax) and sum to b?

9 * 4 = 36

6 * 6 = 36

6 + 6 = 12

so,

4p^2 + 6p + 6p + 9 = 0

(4p^2 + 6p) + (6p + 9)

2p(2p + 3) + 3p(2p + 3)

(2p + 3p) (2p + 3) = 0

2p = -3
p = -3/2

&

2p =- 3
p = -3/2

Or

you can try a square:

(2^2)p^2 + 12p + 3^2 = 0

(2p + 3)^2

(2p + 3) (2p + 3)

4p^2 + 6p + 6p + 9 = 0
4p^2 + 12p + 9 = 0

=(2p+3)^2=0 2p+3=0 2p=-3 p=-3/2=-1.5

4p^2+12p+9=0

4p^2+6p+6p+9=0

2p(2p+3)+3(2p+3)=0

(2p+3)^2=0

p=-3/2

( 2 p + 3 ) ( 2 p + 3 ) = 0

p = - 3/2 (twice)

4p^2 + 12p + 9
= 4p^2 + 6p + 6p + 9
= (4p^2 + 6p) + (6p + 9)
= 2p(2p + 3) + 3(2p + 3)
= (2p + 3)(2p + 3)
= (2p + 3)^2

4p^(2)+12p+9=0

Find the factors such that the product of the factors is the trinomial 4p^(2)+12p+9. This can be done by trial and error and checked using the FOIL method of simplifying polynomials.
(2p+3)(2p+3)=0

Combine the two common factors of (2p+3) by adding the exponents.
(2p+3)^(2)=0

Set each of the factors of the left-hand side of the equation equal to 0.
2p+3=0

Since 3 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 3 from both sides.
2p=-3

Divide each term in the equation by 2.
(2p)/(2)=-(3)/(2)

Simplify the left-hand side of the equation by canceling the common terms.
p=-(3)/(2)

Hope this helps

p=-3/2