3p^2+24p+41=5

Solution for 3p^2+24p+41=5 equation:

Simplifying
3p2 + 24p + 41 = 5

Reorder the terms:
41 + 24p + 3p2 = 5

Solving
41 + 24p + 3p2 = 5

Solving for variable 'p'.

Reorder the terms:
41 + -5 + 24p + 3p2 = 5 + -5

Combine like terms: 41 + -5 = 36
36 + 24p + 3p2 = 5 + -5

Combine like terms: 5 + -5 = 0
36 + 24p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 8p + p2) = 0

Factor a trinomial.
3((6 + p)(2 + p)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + p)' equal to zero and attempt to solve:

Simplifying
6 + p = 0

Solving
6 + p = 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 + p = 0 + -6

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

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

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

Simplifying
2 + p = 0

Solving
2 + p = 0

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

Add '-2' to each side of the equation.
2 + -2 + p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + p = 0 + -2
p = 0 + -2

Combine like terms: 0 + -2 = -2
p = -2

Simplifying
p = -2
Solution
p = {-6, -2}