(p+4)(p-3)=8

Solution for (p+4)(p-3)=8 equation:

Simplifying
(p + 4)(p + -3) = 8

Reorder the terms:
(4 + p)(p + -3) = 8

Reorder the terms:
(4 + p)(-3 + p) = 8

Multiply (4 + p) * (-3 + p)
(4(-3 + p) + p(-3 + p)) = 8
((-3 * 4 + p * 4) + p(-3 + p)) = 8
((-12 + 4p) + p(-3 + p)) = 8
(-12 + 4p + (-3 * p + p * p)) = 8
(-12 + 4p + (-3p + p2)) = 8

Combine like terms: 4p + -3p = 1p
(-12 + 1p + p2) = 8

Solving
-12 + 1p + p2 = 8

Solving for variable 'p'.

Reorder the terms:
-12 + -8 + 1p + p2 = 8 + -8

Combine like terms: -12 + -8 = -20
-20 + 1p + p2 = 8 + -8

Combine like terms: 8 + -8 = 0
-20 + 1p + p2 = 0

Factor a trinomial.
(-5 + -1p)(4 + -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 '(4 + -1p)' equal to zero and attempt to solve:

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1p = 0 + -4
-1p = 0 + -4

Combine like terms: 0 + -4 = -4
-1p = -4

Divide each side by '-1'.
p = 4

Simplifying
p = 4
Solution
p = {-5, 4}