(p+6)(p-2)=-7

Solution for (p+6)(p-2)=-7 equation:

Simplifying
(p + 6)(p + -2) = -7

Reorder the terms:
(6 + p)(p + -2) = -7

Reorder the terms:
(6 + p)(-2 + p) = -7

Multiply (6 + p) * (-2 + p)
(6(-2 + p) + p(-2 + p)) = -7
((-2 * 6 + p * 6) + p(-2 + p)) = -7
((-12 + 6p) + p(-2 + p)) = -7
(-12 + 6p + (-2 * p + p * p)) = -7
(-12 + 6p + (-2p + p2)) = -7

Combine like terms: 6p + -2p = 4p
(-12 + 4p + p2) = -7

Solving
-12 + 4p + p2 = -7

Solving for variable 'p'.

Reorder the terms:
-12 + 7 + 4p + p2 = -7 + 7

Combine like terms: -12 + 7 = -5
-5 + 4p + p2 = -7 + 7

Combine like terms: -7 + 7 = 0
-5 + 4p + p2 = 0

Factor a trinomial.
(-5 + -1p)(1 + -1p) = 0

Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve:

Simplifying
-5 + -1p = 0

Solving
-5 + -1p = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1p = 0 + 5
-1p = 0 + 5

Combine like terms: 0 + 5 = 5
-1p = 5

Divide each side by '-1'.
p = -5

Simplifying
p = -5
Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve:

Simplifying
1 + -1p = 0

Solving
1 + -1p = 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 + -1p = 0 + -1

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

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

Divide each side by '-1'.
p = 1

Simplifying
p = 1
Solution
p = {-5, 1}