-5p(p+2)=2(2p-15)+p

Solution for -5p(p+2)=2(2p-15)+p equation:

Simplifying
-5p(p + 2) = 2(2p + -15) + p

Reorder the terms:
-5p(2 + p) = 2(2p + -15) + p
(2 * -5p + p * -5p) = 2(2p + -15) + p
(-10p + -5p2) = 2(2p + -15) + p

Reorder the terms:
-10p + -5p2 = 2(-15 + 2p) + p
-10p + -5p2 = (-15 * 2 + 2p * 2) + p
-10p + -5p2 = (-30 + 4p) + p

Combine like terms: 4p + p = 5p
-10p + -5p2 = -30 + 5p

Solving
-10p + -5p2 = -30 + 5p

Solving for variable 'p'.

Reorder the terms:
30 + -10p + -5p + -5p2 = -30 + 5p + 30 + -5p

Combine like terms: -10p + -5p = -15p
30 + -15p + -5p2 = -30 + 5p + 30 + -5p

Reorder the terms:
30 + -15p + -5p2 = -30 + 30 + 5p + -5p

Combine like terms: -30 + 30 = 0
30 + -15p + -5p2 = 0 + 5p + -5p
30 + -15p + -5p2 = 5p + -5p

Combine like terms: 5p + -5p = 0
30 + -15p + -5p2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -3p + -1p2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + -3p + -1p2)' equal to zero and attempt to solve:

Simplifying
6 + -3p + -1p2 = 0

Solving
6 + -3p + -1p2 = 0

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

Divide each side by '-1'.
-6 + 3p + p2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3p + 6 + p2 = 0 + 6

Reorder the terms:
-6 + 6 + 3p + p2 = 0 + 6

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

Combine like terms: 0 + 6 = 6
3p + p2 = 6

The p term is 3p.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3p + 2.25 + p2 = 6 + 2.25

Reorder the terms:
2.25 + 3p + p2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + 3p + p2 = 8.25

Factor a perfect square on the left side:
(p + 1.5)(p + 1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(p + 1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
p + 1.5 = 2.872281323

Simplifying
p + 1.5 = 2.872281323

Reorder the terms:
1.5 + p = 2.872281323

Solving
1.5 + p = 2.872281323

Solving for variable 'p'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + p = 2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + p = 2.872281323 + -1.5
p = 2.872281323 + -1.5

Combine like terms: 2.872281323 + -1.5 = 1.372281323
p = 1.372281323

Simplifying
p = 1.372281323

Subproblem 2
p + 1.5 = -2.872281323

Simplifying
p + 1.5 = -2.872281323

Reorder the terms:
1.5 + p = -2.872281323

Solving
1.5 + p = -2.872281323

Solving for variable 'p'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + p = -2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + p = -2.872281323 + -1.5
p = -2.872281323 + -1.5

Combine like terms: -2.872281323 + -1.5 = -4.372281323
p = -4.372281323

Simplifying
p = -4.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.372281323, -4.372281323}
Solution
p = {1.372281323, -4.372281323}