8=6-p(p+3)

Solution for 8=6-p(p+3) equation:

Simplifying
8 = 6 + -1p(p + 3)

Reorder the terms:
8 = 6 + -1p(3 + p)
8 = 6 + (3 * -1p + p * -1p)
8 = 6 + (-3p + -1p2)

Solving
8 = 6 + -3p + -1p2

Solving for variable 'p'.

Combine like terms: 8 + -6 = 2
2 + 3p + p2 = 6 + -3p + -1p2 + -6 + 3p + p2

Reorder the terms:
2 + 3p + p2 = 6 + -6 + -3p + 3p + -1p2 + p2

Combine like terms: 6 + -6 = 0
2 + 3p + p2 = 0 + -3p + 3p + -1p2 + p2
2 + 3p + p2 = -3p + 3p + -1p2 + p2

Combine like terms: -3p + 3p = 0
2 + 3p + p2 = 0 + -1p2 + p2
2 + 3p + p2 = -1p2 + p2

Combine like terms: -1p2 + p2 = 0
2 + 3p + p2 = 0

Factor a trinomial.
(2 + p)(1 + p) = 0

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

Simplifying
2 + p = 0

Solving
2 + p = 0

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

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

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

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

Simplifying
p = -2
Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve:

Simplifying
1 + p = 0

Solving
1 + p = 0

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 = 0 + -1

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

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

Simplifying
p = -1
Solution
p = {-2, -1}