4p+4p(p+5)=10

Solution for 4p+4p(p+5)=10 equation:

Simplifying
4p + 4p(p + 5) = 10

Reorder the terms:
4p + 4p(5 + p) = 10
4p + (5 * 4p + p * 4p) = 10
4p + (20p + 4p2) = 10

Combine like terms: 4p + 20p = 24p
24p + 4p2 = 10

Solving
24p + 4p2 = 10

Solving for variable 'p'.

Reorder the terms:
-10 + 24p + 4p2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 24p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 12p + 2p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 12p + 2p2)' equal to zero and attempt to solve:

Simplifying
-5 + 12p + 2p2 = 0

Solving
-5 + 12p + 2p2 = 0

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

Divide each side by '2'.
-2.5 + 6p + p2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 6p + 2.5 + p2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 6p + p2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 6p + p2 = 0 + 2.5
6p + p2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
6p + p2 = 2.5

The p term is 6p.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6p + 9 + p2 = 2.5 + 9

Reorder the terms:
9 + 6p + p2 = 2.5 + 9

Combine like terms: 2.5 + 9 = 11.5
9 + 6p + p2 = 11.5

Factor a perfect square on the left side:
(p + 3)(p + 3) = 11.5

Calculate the square root of the right side: 3.391164992

Break this problem into two subproblems by setting 
(p + 3) equal to 3.391164992 and -3.391164992.

Subproblem 1
p + 3 = 3.391164992

Simplifying
p + 3 = 3.391164992

Reorder the terms:
3 + p = 3.391164992

Solving
3 + p = 3.391164992

Solving for variable 'p'.

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

Add '-3' to each side of the equation.
3 + -3 + p = 3.391164992 + -3

Combine like terms: 3 + -3 = 0
0 + p = 3.391164992 + -3
p = 3.391164992 + -3

Combine like terms: 3.391164992 + -3 = 0.391164992
p = 0.391164992

Simplifying
p = 0.391164992

Subproblem 2
p + 3 = -3.391164992

Simplifying
p + 3 = -3.391164992

Reorder the terms:
3 + p = -3.391164992

Solving
3 + p = -3.391164992

Solving for variable 'p'.

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

Add '-3' to each side of the equation.
3 + -3 + p = -3.391164992 + -3

Combine like terms: 3 + -3 = 0
0 + p = -3.391164992 + -3
p = -3.391164992 + -3

Combine like terms: -3.391164992 + -3 = -6.391164992
p = -6.391164992

Simplifying
p = -6.391164992

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.391164992, -6.391164992}
Solution
p = {0.391164992, -6.391164992}