(p+2)(p-3)=50

Solution for (p+2)(p-3)=50 equation:

Simplifying
(p + 2)(p + -3) = 50

Reorder the terms:
(2 + p)(p + -3) = 50

Reorder the terms:
(2 + p)(-3 + p) = 50

Multiply (2 + p) * (-3 + p)
(2(-3 + p) + p(-3 + p)) = 50
((-3 * 2 + p * 2) + p(-3 + p)) = 50
((-6 + 2p) + p(-3 + p)) = 50
(-6 + 2p + (-3 * p + p * p)) = 50
(-6 + 2p + (-3p + p2)) = 50

Combine like terms: 2p + -3p = -1p
(-6 + -1p + p2) = 50

Solving
-6 + -1p + p2 = 50

Solving for variable 'p'.

Reorder the terms:
-6 + -50 + -1p + p2 = 50 + -50

Combine like terms: -6 + -50 = -56
-56 + -1p + p2 = 50 + -50

Combine like terms: 50 + -50 = 0
-56 + -1p + p2 = 0

Factor a trinomial.
(-7 + -1p)(8 + -1p) = 0

Subproblem 1
Set the factor '(-7 + -1p)' equal to zero and attempt to solve:

Simplifying
-7 + -1p = 0

Solving
-7 + -1p = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1p = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1p = 0 + 7
-1p = 0 + 7

Combine like terms: 0 + 7 = 7
-1p = 7

Divide each side by '-1'.
p = -7

Simplifying
p = -7
Subproblem 2
Set the factor '(8 + -1p)' equal to zero and attempt to solve:

Simplifying
8 + -1p = 0

Solving
8 + -1p = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1p = 0 + -8

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

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

Divide each side by '-1'.
p = 8

Simplifying
p = 8
Solution
p = {-7, 8}