10-4p(p+7)=2(1-p)

Solution for 10-4p(p+7)=2(1-p) equation:

Simplifying
10 + -4p(p + 7) = 2(1 + -1p)

Reorder the terms:
10 + -4p(7 + p) = 2(1 + -1p)
10 + (7 * -4p + p * -4p) = 2(1 + -1p)
10 + (-28p + -4p2) = 2(1 + -1p)
10 + -28p + -4p2 = (1 * 2 + -1p * 2)
10 + -28p + -4p2 = (2 + -2p)

Solving
10 + -28p + -4p2 = 2 + -2p

Solving for variable 'p'.

Reorder the terms:
10 + -2 + -28p + 2p + -4p2 = 2 + -2p + -2 + 2p

Combine like terms: 10 + -2 = 8
8 + -28p + 2p + -4p2 = 2 + -2p + -2 + 2p

Combine like terms: -28p + 2p = -26p
8 + -26p + -4p2 = 2 + -2p + -2 + 2p

Reorder the terms:
8 + -26p + -4p2 = 2 + -2 + -2p + 2p

Combine like terms: 2 + -2 = 0
8 + -26p + -4p2 = 0 + -2p + 2p
8 + -26p + -4p2 = -2p + 2p

Combine like terms: -2p + 2p = 0
8 + -26p + -4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -13p + -2p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -13p + -2p2)' equal to zero and attempt to solve:

Simplifying
4 + -13p + -2p2 = 0

Solving
4 + -13p + -2p2 = 0

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

Divide each side by '-2'.
-2 + 6.5p + p2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 6.5p + 2 + p2 = 0 + 2

Reorder the terms:
-2 + 2 + 6.5p + p2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 6.5p + p2 = 0 + 2
6.5p + p2 = 0 + 2

Combine like terms: 0 + 2 = 2
6.5p + p2 = 2

The p term is 6.5p.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5p + 10.5625 + p2 = 2 + 10.5625

Reorder the terms:
10.5625 + 6.5p + p2 = 2 + 10.5625

Combine like terms: 2 + 10.5625 = 12.5625
10.5625 + 6.5p + p2 = 12.5625

Factor a perfect square on the left side:
(p + 3.25)(p + 3.25) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(p + 3.25) equal to 3.54436172 and -3.54436172.

Subproblem 1
p + 3.25 = 3.54436172

Simplifying
p + 3.25 = 3.54436172

Reorder the terms:
3.25 + p = 3.54436172

Solving
3.25 + p = 3.54436172

Solving for variable 'p'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + p = 3.54436172 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + p = 3.54436172 + -3.25
p = 3.54436172 + -3.25

Combine like terms: 3.54436172 + -3.25 = 0.29436172
p = 0.29436172

Simplifying
p = 0.29436172

Subproblem 2
p + 3.25 = -3.54436172

Simplifying
p + 3.25 = -3.54436172

Reorder the terms:
3.25 + p = -3.54436172

Solving
3.25 + p = -3.54436172

Solving for variable 'p'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + p = -3.54436172 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + p = -3.54436172 + -3.25
p = -3.54436172 + -3.25

Combine like terms: -3.54436172 + -3.25 = -6.79436172
p = -6.79436172

Simplifying
p = -6.79436172

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.29436172, -6.79436172}
Solution
p = {0.29436172, -6.79436172}