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

Solution for p^2+3p+6=(p+2)(p+9) equation:

Simplifying
p2 + 3p + 6 = (p + 2)(p + 9)

Reorder the terms:
6 + 3p + p2 = (p + 2)(p + 9)

Reorder the terms:
6 + 3p + p2 = (2 + p)(p + 9)

Reorder the terms:
6 + 3p + p2 = (2 + p)(9 + p)

Multiply (2 + p) * (9 + p)
6 + 3p + p2 = (2(9 + p) + p(9 + p))
6 + 3p + p2 = ((9 * 2 + p * 2) + p(9 + p))
6 + 3p + p2 = ((18 + 2p) + p(9 + p))
6 + 3p + p2 = (18 + 2p + (9 * p + p * p))
6 + 3p + p2 = (18 + 2p + (9p + p2))

Combine like terms: 2p + 9p = 11p
6 + 3p + p2 = (18 + 11p + p2)

Add '-1p2' to each side of the equation.
6 + 3p + p2 + -1p2 = 18 + 11p + p2 + -1p2

Combine like terms: p2 + -1p2 = 0
6 + 3p + 0 = 18 + 11p + p2 + -1p2
6 + 3p = 18 + 11p + p2 + -1p2

Combine like terms: p2 + -1p2 = 0
6 + 3p = 18 + 11p + 0
6 + 3p = 18 + 11p

Solving
6 + 3p = 18 + 11p

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-11p' to each side of the equation.
6 + 3p + -11p = 18 + 11p + -11p

Combine like terms: 3p + -11p = -8p
6 + -8p = 18 + 11p + -11p

Combine like terms: 11p + -11p = 0
6 + -8p = 18 + 0
6 + -8p = 18

Add '-6' to each side of the equation.
6 + -6 + -8p = 18 + -6

Combine like terms: 6 + -6 = 0
0 + -8p = 18 + -6
-8p = 18 + -6

Combine like terms: 18 + -6 = 12
-8p = 12

Divide each side by '-8'.
p = -1.5

Simplifying
p = -1.5