3n^2+24n+51=3

Solution for 3n^2+24n+51=3 equation:

Simplifying
3n2 + 24n + 51 = 3

Reorder the terms:
51 + 24n + 3n2 = 3

Solving
51 + 24n + 3n2 = 3

Solving for variable 'n'.

Reorder the terms:
51 + -3 + 24n + 3n2 = 3 + -3

Combine like terms: 51 + -3 = 48
48 + 24n + 3n2 = 3 + -3

Combine like terms: 3 + -3 = 0
48 + 24n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + 8n + n2) = 0

Factor a trinomial.
3((4 + n)(4 + n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {-4, -4}