(8p-7)-(2p^2+6p-9)=0

Solution for (8p-7)-(2p^2+6p-9)=0 equation:

Simplifying
(8p + -7) + -1(2p2 + 6p + -9) = 0

Reorder the terms:
(-7 + 8p) + -1(2p2 + 6p + -9) = 0

Remove parenthesis around (-7 + 8p)
-7 + 8p + -1(2p2 + 6p + -9) = 0

Reorder the terms:
-7 + 8p + -1(-9 + 6p + 2p2) = 0
-7 + 8p + (-9 * -1 + 6p * -1 + 2p2 * -1) = 0
-7 + 8p + (9 + -6p + -2p2) = 0

Reorder the terms:
-7 + 9 + 8p + -6p + -2p2 = 0

Combine like terms: -7 + 9 = 2
2 + 8p + -6p + -2p2 = 0

Combine like terms: 8p + -6p = 2p
2 + 2p + -2p2 = 0

Solving
2 + 2p + -2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + p + -1p2) = 0

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

Simplifying
1 + p + -1p2 = 0

Solving
1 + p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -1p + p2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1p + 1 + p2 = 0 + 1

Reorder the terms:
-1 + 1 + -1p + p2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1p + p2 = 0 + 1
-1p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1p + p2 = 1

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1p + 0.25 + p2 = 1 + 0.25

Reorder the terms:
0.25 + -1p + p2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1p + p2 = 1.25

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(p + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
p + 0.5 = 1.118033989

Simplifying
p + 0.5 = 1.118033989

Reorder the terms:
0.5 + p = 1.118033989

Solving
0.5 + p = 1.118033989

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = 1.118033989 + -0.5
p = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
p = 0.618033989

Simplifying
p = 0.618033989

Subproblem 2
p + 0.5 = -1.118033989

Simplifying
p + 0.5 = -1.118033989

Reorder the terms:
0.5 + p = -1.118033989

Solving
0.5 + p = -1.118033989

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = -1.118033989 + -0.5
p = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
p = -1.618033989

Simplifying
p = -1.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.618033989, -1.618033989}
Solution
p = {0.618033989, -1.618033989}