2n^2+3n=54

Solution for 2n^2+3n=54 equation:

Simplifying
2n2 + 3n = 54

Reorder the terms:
3n + 2n2 = 54

Solving
3n + 2n2 = 54

Solving for variable 'n'.

Reorder the terms:
-54 + 3n + 2n2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 3n + 2n2 = 0

Factor a trinomial.
(-6 + -1n)(9 + -2n) = 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 '(9 + -2n)' equal to zero and attempt to solve:

Simplifying
9 + -2n = 0

Solving
9 + -2n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2n = 0 + -9
-2n = 0 + -9

Combine like terms: 0 + -9 = -9
-2n = -9

Divide each side by '-2'.
n = 4.5

Simplifying
n = 4.5
Solution
n = {-6, 4.5}