7p(5p-8)=28-7p

Solution for 7p(5p-8)=28-7p equation:

Simplifying
7p(5p + -8) = 28 + -7p

Reorder the terms:
7p(-8 + 5p) = 28 + -7p
(-8 * 7p + 5p * 7p) = 28 + -7p
(-56p + 35p2) = 28 + -7p

Solving
-56p + 35p2 = 28 + -7p

Solving for variable 'p'.

Reorder the terms:
-28 + -56p + 7p + 35p2 = 28 + -7p + -28 + 7p

Combine like terms: -56p + 7p = -49p
-28 + -49p + 35p2 = 28 + -7p + -28 + 7p

Reorder the terms:
-28 + -49p + 35p2 = 28 + -28 + -7p + 7p

Combine like terms: 28 + -28 = 0
-28 + -49p + 35p2 = 0 + -7p + 7p
-28 + -49p + 35p2 = -7p + 7p

Combine like terms: -7p + 7p = 0
-28 + -49p + 35p2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-4 + -7p + 5p2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-4 + -7p + 5p2)' equal to zero and attempt to solve:

Simplifying
-4 + -7p + 5p2 = 0

Solving
-4 + -7p + 5p2 = 0

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

Divide each side by '5'.
-0.8 + -1.4p + p2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -1.4p + 0.8 + p2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -1.4p + p2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -1.4p + p2 = 0 + 0.8
-1.4p + p2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-1.4p + p2 = 0.8

The p term is -1.4p.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4p + 0.49 + p2 = 0.8 + 0.49

Reorder the terms:
0.49 + -1.4p + p2 = 0.8 + 0.49

Combine like terms: 0.8 + 0.49 = 1.29
0.49 + -1.4p + p2 = 1.29

Factor a perfect square on the left side:
(p + -0.7)(p + -0.7) = 1.29

Calculate the square root of the right side: 1.135781669

Break this problem into two subproblems by setting 
(p + -0.7) equal to 1.135781669 and -1.135781669.

Subproblem 1
p + -0.7 = 1.135781669

Simplifying
p + -0.7 = 1.135781669

Reorder the terms:
-0.7 + p = 1.135781669

Solving
-0.7 + p = 1.135781669

Solving for variable 'p'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + p = 1.135781669 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + p = 1.135781669 + 0.7
p = 1.135781669 + 0.7

Combine like terms: 1.135781669 + 0.7 = 1.835781669
p = 1.835781669

Simplifying
p = 1.835781669

Subproblem 2
p + -0.7 = -1.135781669

Simplifying
p + -0.7 = -1.135781669

Reorder the terms:
-0.7 + p = -1.135781669

Solving
-0.7 + p = -1.135781669

Solving for variable 'p'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + p = -1.135781669 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + p = -1.135781669 + 0.7
p = -1.135781669 + 0.7

Combine like terms: -1.135781669 + 0.7 = -0.435781669
p = -0.435781669

Simplifying
p = -0.435781669

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.835781669, -0.435781669}
Solution
p = {1.835781669, -0.435781669}