9p(p+1)+13=5(2p+17)-8p

Solution for 9p(p+1)+13=5(2p+17)-8p equation:

Simplifying
9p(p + 1) + 13 = 5(2p + 17) + -8p

Reorder the terms:
9p(1 + p) + 13 = 5(2p + 17) + -8p
(1 * 9p + p * 9p) + 13 = 5(2p + 17) + -8p
(9p + 9p2) + 13 = 5(2p + 17) + -8p

Reorder the terms:
13 + 9p + 9p2 = 5(2p + 17) + -8p

Reorder the terms:
13 + 9p + 9p2 = 5(17 + 2p) + -8p
13 + 9p + 9p2 = (17 * 5 + 2p * 5) + -8p
13 + 9p + 9p2 = (85 + 10p) + -8p

Combine like terms: 10p + -8p = 2p
13 + 9p + 9p2 = 85 + 2p

Solving
13 + 9p + 9p2 = 85 + 2p

Solving for variable 'p'.

Reorder the terms:
13 + -85 + 9p + -2p + 9p2 = 85 + 2p + -85 + -2p

Combine like terms: 13 + -85 = -72
-72 + 9p + -2p + 9p2 = 85 + 2p + -85 + -2p

Combine like terms: 9p + -2p = 7p
-72 + 7p + 9p2 = 85 + 2p + -85 + -2p

Reorder the terms:
-72 + 7p + 9p2 = 85 + -85 + 2p + -2p

Combine like terms: 85 + -85 = 0
-72 + 7p + 9p2 = 0 + 2p + -2p
-72 + 7p + 9p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
-72 + 7p + 9p2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-8 + 0.7777777778p + p2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 0.7777777778p + 8 + p2 = 0 + 8

Reorder the terms:
-8 + 8 + 0.7777777778p + p2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 0.7777777778p + p2 = 0 + 8
0.7777777778p + p2 = 0 + 8

Combine like terms: 0 + 8 = 8
0.7777777778p + p2 = 8

The p term is 0.7777777778p.  Take half its coefficient (0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
0.7777777778p + 0.1512345679 + p2 = 8 + 0.1512345679

Reorder the terms:
0.1512345679 + 0.7777777778p + p2 = 8 + 0.1512345679

Combine like terms: 8 + 0.1512345679 = 8.1512345679
0.1512345679 + 0.7777777778p + p2 = 8.1512345679

Factor a perfect square on the left side:
(p + 0.3888888889)(p + 0.3888888889) = 8.1512345679

Calculate the square root of the right side: 2.855036702

Break this problem into two subproblems by setting 
(p + 0.3888888889) equal to 2.855036702 and -2.855036702.

Subproblem 1
p + 0.3888888889 = 2.855036702

Simplifying
p + 0.3888888889 = 2.855036702

Reorder the terms:
0.3888888889 + p = 2.855036702

Solving
0.3888888889 + p = 2.855036702

Solving for variable 'p'.

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

Add '-0.3888888889' to each side of the equation.
0.3888888889 + -0.3888888889 + p = 2.855036702 + -0.3888888889

Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000
0.0000000000 + p = 2.855036702 + -0.3888888889
p = 2.855036702 + -0.3888888889

Combine like terms: 2.855036702 + -0.3888888889 = 2.4661478131
p = 2.4661478131

Simplifying
p = 2.4661478131

Subproblem 2
p + 0.3888888889 = -2.855036702

Simplifying
p + 0.3888888889 = -2.855036702

Reorder the terms:
0.3888888889 + p = -2.855036702

Solving
0.3888888889 + p = -2.855036702

Solving for variable 'p'.

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

Add '-0.3888888889' to each side of the equation.
0.3888888889 + -0.3888888889 + p = -2.855036702 + -0.3888888889

Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000
0.0000000000 + p = -2.855036702 + -0.3888888889
p = -2.855036702 + -0.3888888889

Combine like terms: -2.855036702 + -0.3888888889 = -3.2439255909
p = -3.2439255909

Simplifying
p = -3.2439255909

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.4661478131, -3.2439255909}