p^2-8p+24=4p-12

Solution for p^2-8p+24=4p-12 equation:

Simplifying
p2 + -8p + 24 = 4p + -12

Reorder the terms:
24 + -8p + p2 = 4p + -12

Reorder the terms:
24 + -8p + p2 = -12 + 4p

Solving
24 + -8p + p2 = -12 + 4p

Solving for variable 'p'.

Reorder the terms:
24 + 12 + -8p + -4p + p2 = -12 + 4p + 12 + -4p

Combine like terms: 24 + 12 = 36
36 + -8p + -4p + p2 = -12 + 4p + 12 + -4p

Combine like terms: -8p + -4p = -12p
36 + -12p + p2 = -12 + 4p + 12 + -4p

Reorder the terms:
36 + -12p + p2 = -12 + 12 + 4p + -4p

Combine like terms: -12 + 12 = 0
36 + -12p + p2 = 0 + 4p + -4p
36 + -12p + p2 = 4p + -4p

Combine like terms: 4p + -4p = 0
36 + -12p + p2 = 0

Factor a trinomial.
(6 + -1p)(6 + -1p) = 0

Subproblem 1
Set the factor '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p = 0 + -6
-1p = 0 + -6

Combine like terms: 0 + -6 = -6
-1p = -6

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Subproblem 2
Set the factor '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p = 0 + -6
-1p = 0 + -6

Combine like terms: 0 + -6 = -6
-1p = -6

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Solution
p = {6, 6}