10p+9-11-p=-2(2p+4)3(2p-2)

Solution for 10p+9-11-p=-2(2p+4)3(2p-2) equation:

Simplifying
10p + 9 + -11 + -1p = -2(2p + 4) * 3(2p + -2)

Reorder the terms:
9 + -11 + 10p + -1p = -2(2p + 4) * 3(2p + -2)

Combine like terms: 9 + -11 = -2
-2 + 10p + -1p = -2(2p + 4) * 3(2p + -2)

Combine like terms: 10p + -1p = 9p
-2 + 9p = -2(2p + 4) * 3(2p + -2)

Reorder the terms:
-2 + 9p = -2(4 + 2p) * 3(2p + -2)

Reorder the terms:
-2 + 9p = -2(4 + 2p) * 3(-2 + 2p)

Reorder the terms for easier multiplication:
-2 + 9p = -2 * 3(4 + 2p)(-2 + 2p)

Multiply -2 * 3
-2 + 9p = -6(4 + 2p)(-2 + 2p)

Multiply (4 + 2p) * (-2 + 2p)
-2 + 9p = -6(4(-2 + 2p) + 2p * (-2 + 2p))
-2 + 9p = -6((-2 * 4 + 2p * 4) + 2p * (-2 + 2p))
-2 + 9p = -6((-8 + 8p) + 2p * (-2 + 2p))
-2 + 9p = -6(-8 + 8p + (-2 * 2p + 2p * 2p))
-2 + 9p = -6(-8 + 8p + (-4p + 4p2))

Combine like terms: 8p + -4p = 4p
-2 + 9p = -6(-8 + 4p + 4p2)
-2 + 9p = (-8 * -6 + 4p * -6 + 4p2 * -6)
-2 + 9p = (48 + -24p + -24p2)

Solving
-2 + 9p = 48 + -24p + -24p2

Solving for variable 'p'.

Reorder the terms:
-2 + -48 + 9p + 24p + 24p2 = 48 + -24p + -24p2 + -48 + 24p + 24p2

Combine like terms: -2 + -48 = -50
-50 + 9p + 24p + 24p2 = 48 + -24p + -24p2 + -48 + 24p + 24p2

Combine like terms: 9p + 24p = 33p
-50 + 33p + 24p2 = 48 + -24p + -24p2 + -48 + 24p + 24p2

Reorder the terms:
-50 + 33p + 24p2 = 48 + -48 + -24p + 24p + -24p2 + 24p2

Combine like terms: 48 + -48 = 0
-50 + 33p + 24p2 = 0 + -24p + 24p + -24p2 + 24p2
-50 + 33p + 24p2 = -24p + 24p + -24p2 + 24p2

Combine like terms: -24p + 24p = 0
-50 + 33p + 24p2 = 0 + -24p2 + 24p2
-50 + 33p + 24p2 = -24p2 + 24p2

Combine like terms: -24p2 + 24p2 = 0
-50 + 33p + 24p2 = 0

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

Divide each side by '24'.
-2.083333333 + 1.375p + p2 = 0

Move the constant term to the right:

Add '2.083333333' to each side of the equation.
-2.083333333 + 1.375p + 2.083333333 + p2 = 0 + 2.083333333

Reorder the terms:
-2.083333333 + 2.083333333 + 1.375p + p2 = 0 + 2.083333333

Combine like terms: -2.083333333 + 2.083333333 = 0.000000000
0.000000000 + 1.375p + p2 = 0 + 2.083333333
1.375p + p2 = 0 + 2.083333333

Combine like terms: 0 + 2.083333333 = 2.083333333
1.375p + p2 = 2.083333333

The p term is 1.375p.  Take half its coefficient (0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
1.375p + 0.47265625 + p2 = 2.083333333 + 0.47265625

Reorder the terms:
0.47265625 + 1.375p + p2 = 2.083333333 + 0.47265625

Combine like terms: 2.083333333 + 0.47265625 = 2.555989583
0.47265625 + 1.375p + p2 = 2.555989583

Factor a perfect square on the left side:
(p + 0.6875)(p + 0.6875) = 2.555989583

Calculate the square root of the right side: 1.598746253

Break this problem into two subproblems by setting 
(p + 0.6875) equal to 1.598746253 and -1.598746253.

Subproblem 1
p + 0.6875 = 1.598746253

Simplifying
p + 0.6875 = 1.598746253

Reorder the terms:
0.6875 + p = 1.598746253

Solving
0.6875 + p = 1.598746253

Solving for variable 'p'.

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

Add '-0.6875' to each side of the equation.
0.6875 + -0.6875 + p = 1.598746253 + -0.6875

Combine like terms: 0.6875 + -0.6875 = 0.0000
0.0000 + p = 1.598746253 + -0.6875
p = 1.598746253 + -0.6875

Combine like terms: 1.598746253 + -0.6875 = 0.911246253
p = 0.911246253

Simplifying
p = 0.911246253

Subproblem 2
p + 0.6875 = -1.598746253

Simplifying
p + 0.6875 = -1.598746253

Reorder the terms:
0.6875 + p = -1.598746253

Solving
0.6875 + p = -1.598746253

Solving for variable 'p'.

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

Add '-0.6875' to each side of the equation.
0.6875 + -0.6875 + p = -1.598746253 + -0.6875

Combine like terms: 0.6875 + -0.6875 = 0.0000
0.0000 + p = -1.598746253 + -0.6875
p = -1.598746253 + -0.6875

Combine like terms: -1.598746253 + -0.6875 = -2.286246253
p = -2.286246253

Simplifying
p = -2.286246253

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.911246253, -2.286246253}