0.142857p(14-7p)-2=-2(.5p+3)+6

Solution for 0.142857p(14-7p)-2=-2(.5p+3)+6 equation:

Simplifying
0.142857p(14 + -7p) + -2 = -2(0.5p + 3) + 6
(14 * 0.142857p + -7p * 0.142857p) + -2 = -2(0.5p + 3) + 6
(1.999998p + -0.999999p2) + -2 = -2(0.5p + 3) + 6

Reorder the terms:
-2 + 1.999998p + -0.999999p2 = -2(0.5p + 3) + 6

Reorder the terms:
-2 + 1.999998p + -0.999999p2 = -2(3 + 0.5p) + 6
-2 + 1.999998p + -0.999999p2 = (3 * -2 + 0.5p * -2) + 6
-2 + 1.999998p + -0.999999p2 = (-6 + -1p) + 6

Reorder the terms:
-2 + 1.999998p + -0.999999p2 = -6 + 6 + -1p

Combine like terms: -6 + 6 = 0
-2 + 1.999998p + -0.999999p2 = 0 + -1p
-2 + 1.999998p + -0.999999p2 = -1p

Solving
-2 + 1.999998p + -0.999999p2 = -1p

Solving for variable 'p'.

Reorder the terms:
-2 + 1.999998p + p + -0.999999p2 = -1p + p

Combine like terms: 1.999998p + p = 2.999998p
-2 + 2.999998p + -0.999999p2 = -1p + p

Combine like terms: -1p + p = 0
-2 + 2.999998p + -0.999999p2 = 0

Begin completing the square.  Divide all terms by
-0.999999 the coefficient of the squared term: 

Divide each side by '-0.999999'.
2.000002 + -3.000001p + p2 = 0

Move the constant term to the right:

Add '-2.000002' to each side of the equation.
2.000002 + -3.000001p + -2.000002 + p2 = 0 + -2.000002

Reorder the terms:
2.000002 + -2.000002 + -3.000001p + p2 = 0 + -2.000002

Combine like terms: 2.000002 + -2.000002 = 0.000000
0.000000 + -3.000001p + p2 = 0 + -2.000002
-3.000001p + p2 = 0 + -2.000002

Combine like terms: 0 + -2.000002 = -2.000002
-3.000001p + p2 = -2.000002

The p term is -3.000001p.  Take half its coefficient (-1.5000005).
Square it (2.250001500) and add it to both sides.

Add '2.250001500' to each side of the equation.
-3.000001p + 2.250001500 + p2 = -2.000002 + 2.250001500

Reorder the terms:
2.250001500 + -3.000001p + p2 = -2.000002 + 2.250001500

Combine like terms: -2.000002 + 2.250001500 = 0.2499995
2.250001500 + -3.000001p + p2 = 0.2499995

Factor a perfect square on the left side:
(p + -1.5000005)(p + -1.5000005) = 0.2499995

Calculate the square root of the right side: 0.4999995

Break this problem into two subproblems by setting 
(p + -1.5000005) equal to 0.4999995 and -0.4999995.

Subproblem 1
p + -1.5000005 = 0.4999995

Simplifying
p + -1.5000005 = 0.4999995

Reorder the terms:
-1.5000005 + p = 0.4999995

Solving
-1.5000005 + p = 0.4999995

Solving for variable 'p'.

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

Add '1.5000005' to each side of the equation.
-1.5000005 + 1.5000005 + p = 0.4999995 + 1.5000005

Combine like terms: -1.5000005 + 1.5000005 = 0.0000000
0.0000000 + p = 0.4999995 + 1.5000005
p = 0.4999995 + 1.5000005

Combine like terms: 0.4999995 + 1.5000005 = 2
p = 2

Simplifying
p = 2

Subproblem 2
p + -1.5000005 = -0.4999995

Simplifying
p + -1.5000005 = -0.4999995

Reorder the terms:
-1.5000005 + p = -0.4999995

Solving
-1.5000005 + p = -0.4999995

Solving for variable 'p'.

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

Add '1.5000005' to each side of the equation.
-1.5000005 + 1.5000005 + p = -0.4999995 + 1.5000005

Combine like terms: -1.5000005 + 1.5000005 = 0.0000000
0.0000000 + p = -0.4999995 + 1.5000005
p = -0.4999995 + 1.5000005

Combine like terms: -0.4999995 + 1.5000005 = 1.000001
p = 1.000001

Simplifying
p = 1.000001

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2, 1.000001}