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

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

Simplifying
6(7p + -6) + 7p(p + -8) = 0

Reorder the terms:
6(-6 + 7p) + 7p(p + -8) = 0
(-6 * 6 + 7p * 6) + 7p(p + -8) = 0
(-36 + 42p) + 7p(p + -8) = 0

Reorder the terms:
-36 + 42p + 7p(-8 + p) = 0
-36 + 42p + (-8 * 7p + p * 7p) = 0
-36 + 42p + (-56p + 7p2) = 0

Combine like terms: 42p + -56p = -14p
-36 + -14p + 7p2 = 0

Solving
-36 + -14p + 7p2 = 0

Solving for variable 'p'.

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

Divide each side by '7'.
-5.142857143 + -2p + p2 = 0

Move the constant term to the right:

Add '5.142857143' to each side of the equation.
-5.142857143 + -2p + 5.142857143 + p2 = 0 + 5.142857143

Reorder the terms:
-5.142857143 + 5.142857143 + -2p + p2 = 0 + 5.142857143

Combine like terms: -5.142857143 + 5.142857143 = 0.000000000
0.000000000 + -2p + p2 = 0 + 5.142857143
-2p + p2 = 0 + 5.142857143

Combine like terms: 0 + 5.142857143 = 5.142857143
-2p + p2 = 5.142857143

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = 5.142857143 + 1

Reorder the terms:
1 + -2p + p2 = 5.142857143 + 1

Combine like terms: 5.142857143 + 1 = 6.142857143
1 + -2p + p2 = 6.142857143

Factor a perfect square on the left side:
(p + -1)(p + -1) = 6.142857143

Calculate the square root of the right side: 2.478478796

Break this problem into two subproblems by setting 
(p + -1) equal to 2.478478796 and -2.478478796.

Subproblem 1
p + -1 = 2.478478796

Simplifying
p + -1 = 2.478478796

Reorder the terms:
-1 + p = 2.478478796

Solving
-1 + p = 2.478478796

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = 2.478478796 + 1

Combine like terms: -1 + 1 = 0
0 + p = 2.478478796 + 1
p = 2.478478796 + 1

Combine like terms: 2.478478796 + 1 = 3.478478796
p = 3.478478796

Simplifying
p = 3.478478796

Subproblem 2
p + -1 = -2.478478796

Simplifying
p + -1 = -2.478478796

Reorder the terms:
-1 + p = -2.478478796

Solving
-1 + p = -2.478478796

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = -2.478478796 + 1

Combine like terms: -1 + 1 = 0
0 + p = -2.478478796 + 1
p = -2.478478796 + 1

Combine like terms: -2.478478796 + 1 = -1.478478796
p = -1.478478796

Simplifying
p = -1.478478796

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.478478796, -1.478478796}