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

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


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

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

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

Multiply (-3 + p) * (-8 + p)
(-3(-8 + p) + p(-8 + p)) = -4
((-8 * -3 + p * -3) + p(-8 + p)) = -4
((24 + -3p) + p(-8 + p)) = -4
(24 + -3p + (-8 * p + p * p)) = -4
(24 + -3p + (-8p + p2)) = -4

Combine like terms: -3p + -8p = -11p
(24 + -11p + p2) = -4

Solving
24 + -11p + p2 = -4

Solving for variable 'p'.

Reorder the terms:
24 + 4 + -11p + p2 = -4 + 4

Combine like terms: 24 + 4 = 28
28 + -11p + p2 = -4 + 4

Combine like terms: -4 + 4 = 0
28 + -11p + p2 = 0

Factor a trinomial.
(4 + -1p)(7 + -1p) = 0


Subproblem 1
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

Subproblem 2
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
Solution
p = {4, 7}

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