3n^2-84=-4n

Solution for 3n^2-84=-4n equation:

Simplifying
3n2 + -84 = -4n

Reorder the terms:
-84 + 3n2 = -4n

Solving
-84 + 3n2 = -4n

Solving for variable 'n'.

Reorder the terms:
-84 + 4n + 3n2 = -4n + 4n

Combine like terms: -4n + 4n = 0
-84 + 4n + 3n2 = 0

Factor a trinomial.
(-6 + -1n)(14 + -3n) = 0

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

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

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

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

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

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

Simplifying
n = -6
Subproblem 2
Set the factor '(14 + -3n)' equal to zero and attempt to solve:

Simplifying
14 + -3n = 0

Solving
14 + -3n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3n = 0 + -14
-3n = 0 + -14

Combine like terms: 0 + -14 = -14
-3n = -14

Divide each side by '-3'.
n = 4.666666667

Simplifying
n = 4.666666667
Solution
n = {-6, 4.666666667}