p(5p+2)-7(4-2p)=

Solution for p(5p+2)-7(4-2p)= equation:

Simplifying
p(5p + 2) + -7(4 + -2p) = 0

Reorder the terms:
p(2 + 5p) + -7(4 + -2p) = 0
(2 * p + 5p * p) + -7(4 + -2p) = 0
(2p + 5p2) + -7(4 + -2p) = 0
2p + 5p2 + (4 * -7 + -2p * -7) = 0
2p + 5p2 + (-28 + 14p) = 0

Reorder the terms:
-28 + 2p + 14p + 5p2 = 0

Combine like terms: 2p + 14p = 16p
-28 + 16p + 5p2 = 0

Solving
-28 + 16p + 5p2 = 0

Solving for variable 'p'.

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

Divide each side by '5'.
-5.6 + 3.2p + p2 = 0

Move the constant term to the right:

Add '5.6' to each side of the equation.
-5.6 + 3.2p + 5.6 + p2 = 0 + 5.6

Reorder the terms:
-5.6 + 5.6 + 3.2p + p2 = 0 + 5.6

Combine like terms: -5.6 + 5.6 = 0.0
0.0 + 3.2p + p2 = 0 + 5.6
3.2p + p2 = 0 + 5.6

Combine like terms: 0 + 5.6 = 5.6
3.2p + p2 = 5.6

The p term is 3.2p.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2p + 2.56 + p2 = 5.6 + 2.56

Reorder the terms:
2.56 + 3.2p + p2 = 5.6 + 2.56

Combine like terms: 5.6 + 2.56 = 8.16
2.56 + 3.2p + p2 = 8.16

Factor a perfect square on the left side:
(p + 1.6)(p + 1.6) = 8.16

Calculate the square root of the right side: 2.856571371

Break this problem into two subproblems by setting 
(p + 1.6) equal to 2.856571371 and -2.856571371.

Subproblem 1
p + 1.6 = 2.856571371

Simplifying
p + 1.6 = 2.856571371

Reorder the terms:
1.6 + p = 2.856571371

Solving
1.6 + p = 2.856571371

Solving for variable 'p'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + p = 2.856571371 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + p = 2.856571371 + -1.6
p = 2.856571371 + -1.6

Combine like terms: 2.856571371 + -1.6 = 1.256571371
p = 1.256571371

Simplifying
p = 1.256571371

Subproblem 2
p + 1.6 = -2.856571371

Simplifying
p + 1.6 = -2.856571371

Reorder the terms:
1.6 + p = -2.856571371

Solving
1.6 + p = -2.856571371

Solving for variable 'p'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + p = -2.856571371 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + p = -2.856571371 + -1.6
p = -2.856571371 + -1.6

Combine like terms: -2.856571371 + -1.6 = -4.456571371
p = -4.456571371

Simplifying
p = -4.456571371

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.256571371, -4.456571371}