(p-7)(p+3)=24

Solution for (p-7)(p+3)=24 equation:

Simplifying
(p + -7)(p + 3) = 24

Reorder the terms:
(-7 + p)(p + 3) = 24

Reorder the terms:
(-7 + p)(3 + p) = 24

Multiply (-7 + p) * (3 + p)
(-7(3 + p) + p(3 + p)) = 24
((3 * -7 + p * -7) + p(3 + p)) = 24
((-21 + -7p) + p(3 + p)) = 24
(-21 + -7p + (3 * p + p * p)) = 24
(-21 + -7p + (3p + p2)) = 24

Combine like terms: -7p + 3p = -4p
(-21 + -4p + p2) = 24

Solving
-21 + -4p + p2 = 24

Solving for variable 'p'.

Reorder the terms:
-21 + -24 + -4p + p2 = 24 + -24

Combine like terms: -21 + -24 = -45
-45 + -4p + p2 = 24 + -24

Combine like terms: 24 + -24 = 0
-45 + -4p + p2 = 0

Factor a trinomial.
(-5 + -1p)(9 + -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 '(9 + -1p)' equal to zero and attempt to solve:

Simplifying
9 + -1p = 0

Solving
9 + -1p = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1p = 0 + -9
-1p = 0 + -9

Combine like terms: 0 + -9 = -9
-1p = -9

Divide each side by '-1'.
p = 9

Simplifying
p = 9
Solution
p = {-5, 9}