6(-6-7p)-10p(p+8)=

Solution for 6(-6-7p)-10p(p+8)= equation:

Simplifying
6(-6 + -7p) + -10p(p + 8) = 0
(-6 * 6 + -7p * 6) + -10p(p + 8) = 0
(-36 + -42p) + -10p(p + 8) = 0

Reorder the terms:
-36 + -42p + -10p(8 + p) = 0
-36 + -42p + (8 * -10p + p * -10p) = 0
-36 + -42p + (-80p + -10p2) = 0

Combine like terms: -42p + -80p = -122p
-36 + -122p + -10p2 = 0

Solving
-36 + -122p + -10p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(18 + 61p + 5p2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(18 + 61p + 5p2)' equal to zero and attempt to solve:

Simplifying
18 + 61p + 5p2 = 0

Solving
18 + 61p + 5p2 = 0

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

Divide each side by '5'.
3.6 + 12.2p + p2 = 0

Move the constant term to the right:

Add '-3.6' to each side of the equation.
3.6 + 12.2p + -3.6 + p2 = 0 + -3.6

Reorder the terms:
3.6 + -3.6 + 12.2p + p2 = 0 + -3.6

Combine like terms: 3.6 + -3.6 = 0.0
0.0 + 12.2p + p2 = 0 + -3.6
12.2p + p2 = 0 + -3.6

Combine like terms: 0 + -3.6 = -3.6
12.2p + p2 = -3.6

The p term is 12.2p.  Take half its coefficient (6.1).
Square it (37.21) and add it to both sides.

Add '37.21' to each side of the equation.
12.2p + 37.21 + p2 = -3.6 + 37.21

Reorder the terms:
37.21 + 12.2p + p2 = -3.6 + 37.21

Combine like terms: -3.6 + 37.21 = 33.61
37.21 + 12.2p + p2 = 33.61

Factor a perfect square on the left side:
(p + 6.1)(p + 6.1) = 33.61

Calculate the square root of the right side: 5.797413216

Break this problem into two subproblems by setting 
(p + 6.1) equal to 5.797413216 and -5.797413216.

Subproblem 1
p + 6.1 = 5.797413216

Simplifying
p + 6.1 = 5.797413216

Reorder the terms:
6.1 + p = 5.797413216

Solving
6.1 + p = 5.797413216

Solving for variable 'p'.

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

Add '-6.1' to each side of the equation.
6.1 + -6.1 + p = 5.797413216 + -6.1

Combine like terms: 6.1 + -6.1 = 0.0
0.0 + p = 5.797413216 + -6.1
p = 5.797413216 + -6.1

Combine like terms: 5.797413216 + -6.1 = -0.302586784
p = -0.302586784

Simplifying
p = -0.302586784

Subproblem 2
p + 6.1 = -5.797413216

Simplifying
p + 6.1 = -5.797413216

Reorder the terms:
6.1 + p = -5.797413216

Solving
6.1 + p = -5.797413216

Solving for variable 'p'.

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

Add '-6.1' to each side of the equation.
6.1 + -6.1 + p = -5.797413216 + -6.1

Combine like terms: 6.1 + -6.1 = 0.0
0.0 + p = -5.797413216 + -6.1
p = -5.797413216 + -6.1

Combine like terms: -5.797413216 + -6.1 = -11.897413216
p = -11.897413216

Simplifying
p = -11.897413216

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.302586784, -11.897413216}
Solution
p = {-0.302586784, -11.897413216}