p^2-12p+38=3

Solution for p^2-12p+38=3 equation:

Simplifying
p2 + -12p + 38 = 3

Reorder the terms:
38 + -12p + p2 = 3

Solving
38 + -12p + p2 = 3

Solving for variable 'p'.

Reorder the terms:
38 + -3 + -12p + p2 = 3 + -3

Combine like terms: 38 + -3 = 35
35 + -12p + p2 = 3 + -3

Combine like terms: 3 + -3 = 0
35 + -12p + p2 = 0

Factor a trinomial.
(5 + -1p)(7 + -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 '(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 = {5, 7}