38=2(p+5)p

Solution for 38=2(p+5)p equation:

Simplifying
38 = 2(p + 5) * p

Reorder the terms:
38 = 2(5 + p) * p

Reorder the terms for easier multiplication:
38 = 2p(5 + p)
38 = (5 * 2p + p * 2p)
38 = (10p + 2p2)

Solving
38 = 10p + 2p2

Solving for variable 'p'.

Reorder the terms:
38 + -10p + -2p2 = 10p + -10p + 2p2 + -2p2

Combine like terms: 10p + -10p = 0
38 + -10p + -2p2 = 0 + 2p2 + -2p2
38 + -10p + -2p2 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
38 + -10p + -2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(19 + -5p + -1p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(19 + -5p + -1p2)' equal to zero and attempt to solve:

Simplifying
19 + -5p + -1p2 = 0

Solving
19 + -5p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-19 + 5p + p2 = 0

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 5p + 19 + p2 = 0 + 19

Reorder the terms:
-19 + 19 + 5p + p2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 5p + p2 = 0 + 19
5p + p2 = 0 + 19

Combine like terms: 0 + 19 = 19
5p + p2 = 19

The p term is 5p.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5p + 6.25 + p2 = 19 + 6.25

Reorder the terms:
6.25 + 5p + p2 = 19 + 6.25

Combine like terms: 19 + 6.25 = 25.25
6.25 + 5p + p2 = 25.25

Factor a perfect square on the left side:
(p + 2.5)(p + 2.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(p + 2.5) equal to 5.024937811 and -5.024937811.

Subproblem 1
p + 2.5 = 5.024937811

Simplifying
p + 2.5 = 5.024937811

Reorder the terms:
2.5 + p = 5.024937811

Solving
2.5 + p = 5.024937811

Solving for variable 'p'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + p = 5.024937811 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = 5.024937811 + -2.5
p = 5.024937811 + -2.5

Combine like terms: 5.024937811 + -2.5 = 2.524937811
p = 2.524937811

Simplifying
p = 2.524937811

Subproblem 2
p + 2.5 = -5.024937811

Simplifying
p + 2.5 = -5.024937811

Reorder the terms:
2.5 + p = -5.024937811

Solving
2.5 + p = -5.024937811

Solving for variable 'p'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + p = -5.024937811 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = -5.024937811 + -2.5
p = -5.024937811 + -2.5

Combine like terms: -5.024937811 + -2.5 = -7.524937811
p = -7.524937811

Simplifying
p = -7.524937811

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.524937811, -7.524937811}
Solution
p = {2.524937811, -7.524937811}