5[2p-4p(p+5)]=25

Solution for 5[2p-4p(p+5)]=25 equation:

Simplifying
5[2p + -4p(p + 5)] = 25

Reorder the terms:
5[2p + -4p(5 + p)] = 25
5[2p + (5 * -4p + p * -4p)] = 25
5[2p + (-20p + -4p2)] = 25

Combine like terms: 2p + -20p = -18p
5[-18p + -4p2] = 25
[-18p * 5 + -4p2 * 5] = 25
[-90p + -20p2] = 25

Solving
-90p + -20p2 = 25

Solving for variable 'p'.

Reorder the terms:
-25 + -90p + -20p2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -90p + -20p2 = 0

Factor out the Greatest Common Factor (GCF), '-5'.
-5(5 + 18p + 4p2) = 0

Ignore the factor -5.
Subproblem 1
Set the factor '(5 + 18p + 4p2)' equal to zero and attempt to solve:

Simplifying
5 + 18p + 4p2 = 0

Solving
5 + 18p + 4p2 = 0

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

Divide each side by '4'.
1.25 + 4.5p + p2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 4.5p + -1.25 + p2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 4.5p + p2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 4.5p + p2 = 0 + -1.25
4.5p + p2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
4.5p + p2 = -1.25

The p term is 4.5p.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5p + 5.0625 + p2 = -1.25 + 5.0625

Reorder the terms:
5.0625 + 4.5p + p2 = -1.25 + 5.0625

Combine like terms: -1.25 + 5.0625 = 3.8125
5.0625 + 4.5p + p2 = 3.8125

Factor a perfect square on the left side:
(p + 2.25)(p + 2.25) = 3.8125

Calculate the square root of the right side: 1.952562419

Break this problem into two subproblems by setting 
(p + 2.25) equal to 1.952562419 and -1.952562419.

Subproblem 1
p + 2.25 = 1.952562419

Simplifying
p + 2.25 = 1.952562419

Reorder the terms:
2.25 + p = 1.952562419

Solving
2.25 + p = 1.952562419

Solving for variable 'p'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + p = 1.952562419 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + p = 1.952562419 + -2.25
p = 1.952562419 + -2.25

Combine like terms: 1.952562419 + -2.25 = -0.297437581
p = -0.297437581

Simplifying
p = -0.297437581

Subproblem 2
p + 2.25 = -1.952562419

Simplifying
p + 2.25 = -1.952562419

Reorder the terms:
2.25 + p = -1.952562419

Solving
2.25 + p = -1.952562419

Solving for variable 'p'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + p = -1.952562419 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + p = -1.952562419 + -2.25
p = -1.952562419 + -2.25

Combine like terms: -1.952562419 + -2.25 = -4.202562419
p = -4.202562419

Simplifying
p = -4.202562419

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.297437581, -4.202562419}
Solution
p = {-0.297437581, -4.202562419}