-2p(p+7)-2(2p+6)-6=

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Solution for -2p(p+7)-2(2p+6)-6= equation: 


Simplifying
-2p(p + 7) + -2(2p + 6) + -6 = 0

Reorder the terms:
-2p(7 + p) + -2(2p + 6) + -6 = 0
(7 * -2p + p * -2p) + -2(2p + 6) + -6 = 0
(-14p + -2p2) + -2(2p + 6) + -6 = 0

Reorder the terms:
-14p + -2p2 + -2(6 + 2p) + -6 = 0
-14p + -2p2 + (6 * -2 + 2p * -2) + -6 = 0
-14p + -2p2 + (-12 + -4p) + -6 = 0

Reorder the terms:
-12 + -6 + -14p + -4p + -2p2 = 0

Combine like terms: -12 + -6 = -18
-18 + -14p + -4p + -2p2 = 0

Combine like terms: -14p + -4p = -18p
-18 + -18p + -2p2 = 0

Solving
-18 + -18p + -2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(9 + 9p + p2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(9 + 9p + p2)' equal to zero and attempt to solve:

Simplifying
9 + 9p + p2 = 0

Solving
9 + 9p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 9p + -9 + p2 = 0 + -9

Reorder the terms:
9 + -9 + 9p + p2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 9p + p2 = 0 + -9
9p + p2 = 0 + -9

Combine like terms: 0 + -9 = -9
9p + p2 = -9

The p term is 9p.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9p + 20.25 + p2 = -9 + 20.25

Reorder the terms:
20.25 + 9p + p2 = -9 + 20.25

Combine like terms: -9 + 20.25 = 11.25
20.25 + 9p + p2 = 11.25

Factor a perfect square on the left side:
(p + 4.5)(p + 4.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(p + 4.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
p + 4.5 = 3.354101966

Simplifying
p + 4.5 = 3.354101966

Reorder the terms:
4.5 + p = 3.354101966

Solving
4.5 + p = 3.354101966

Solving for variable 'p'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + p = 3.354101966 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + p = 3.354101966 + -4.5
p = 3.354101966 + -4.5

Combine like terms: 3.354101966 + -4.5 = -1.145898034
p = -1.145898034

Simplifying
p = -1.145898034


Subproblem 2
p + 4.5 = -3.354101966

Simplifying
p + 4.5 = -3.354101966

Reorder the terms:
4.5 + p = -3.354101966

Solving
4.5 + p = -3.354101966

Solving for variable 'p'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + p = -3.354101966 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + p = -3.354101966 + -4.5
p = -3.354101966 + -4.5

Combine like terms: -3.354101966 + -4.5 = -7.854101966
p = -7.854101966

Simplifying
p = -7.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-1.145898034, -7.854101966}
Solution
p = {-1.145898034, -7.854101966}

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