(p-1)(p-4)=28

Solution for (p-1)(p-4)=28 equation:

Simplifying
(p + -1)(p + -4) = 28

Reorder the terms:
(-1 + p)(p + -4) = 28

Reorder the terms:
(-1 + p)(-4 + p) = 28

Multiply (-1 + p) * (-4 + p)
(-1(-4 + p) + p(-4 + p)) = 28
((-4 * -1 + p * -1) + p(-4 + p)) = 28
((4 + -1p) + p(-4 + p)) = 28
(4 + -1p + (-4 * p + p * p)) = 28
(4 + -1p + (-4p + p2)) = 28

Combine like terms: -1p + -4p = -5p
(4 + -5p + p2) = 28

Solving
4 + -5p + p2 = 28

Solving for variable 'p'.

Reorder the terms:
4 + -28 + -5p + p2 = 28 + -28

Combine like terms: 4 + -28 = -24
-24 + -5p + p2 = 28 + -28

Combine like terms: 28 + -28 = 0
-24 + -5p + p2 = 0

Factor a trinomial.
(-3 + -1p)(8 + -1p) = 0

Subproblem 1
Set the factor '(-3 + -1p)' equal to zero and attempt to solve:

Simplifying
-3 + -1p = 0

Solving
-3 + -1p = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1p = 0 + 3

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

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

Divide each side by '-1'.
p = -3

Simplifying
p = -3
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 = {-3, 8}