p+1(p+3)(p+7)=

Solution for p+1(p+3)(p+7)= equation:

Simplifying
p + 1(p + 3)(p + 7) = 0

Reorder the terms:
p + 1(3 + p)(p + 7) = 0

Reorder the terms:
p + 1(3 + p)(7 + p) = 0

Multiply (3 + p) * (7 + p)
p + 1(3(7 + p) + p(7 + p)) = 0
p + 1((7 * 3 + p * 3) + p(7 + p)) = 0
p + 1((21 + 3p) + p(7 + p)) = 0
p + 1(21 + 3p + (7 * p + p * p)) = 0
p + 1(21 + 3p + (7p + p2)) = 0

Combine like terms: 3p + 7p = 10p
p + 1(21 + 10p + p2) = 0
p + (21 * 1 + 10p * 1 + p2 * 1) = 0
p + (21 + 10p + 1p2) = 0

Reorder the terms:
21 + p + 10p + 1p2 = 0

Combine like terms: p + 10p = 11p
21 + 11p + 1p2 = 0

Solving
21 + 11p + 1p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 11p + -21 + p2 = 0 + -21

Reorder the terms:
21 + -21 + 11p + p2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 11p + p2 = 0 + -21
11p + p2 = 0 + -21

Combine like terms: 0 + -21 = -21
11p + p2 = -21

The p term is 11p.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11p + 30.25 + p2 = -21 + 30.25

Reorder the terms:
30.25 + 11p + p2 = -21 + 30.25

Combine like terms: -21 + 30.25 = 9.25
30.25 + 11p + p2 = 9.25

Factor a perfect square on the left side:
(p + 5.5)(p + 5.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(p + 5.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
p + 5.5 = 3.041381265

Simplifying
p + 5.5 = 3.041381265

Reorder the terms:
5.5 + p = 3.041381265

Solving
5.5 + p = 3.041381265

Solving for variable 'p'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + p = 3.041381265 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + p = 3.041381265 + -5.5
p = 3.041381265 + -5.5

Combine like terms: 3.041381265 + -5.5 = -2.458618735
p = -2.458618735

Simplifying
p = -2.458618735

Subproblem 2
p + 5.5 = -3.041381265

Simplifying
p + 5.5 = -3.041381265

Reorder the terms:
5.5 + p = -3.041381265

Solving
5.5 + p = -3.041381265

Solving for variable 'p'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + p = -3.041381265 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + p = -3.041381265 + -5.5
p = -3.041381265 + -5.5

Combine like terms: -3.041381265 + -5.5 = -8.541381265
p = -8.541381265

Simplifying
p = -8.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-2.458618735, -8.541381265}