2n^2=46n+48

Solution for 2n^2=46n+48 equation:

Simplifying
2n2 = 46n + 48

Reorder the terms:
2n2 = 48 + 46n

Solving
2n2 = 48 + 46n

Solving for variable 'n'.

Reorder the terms:
-48 + -46n + 2n2 = 48 + 46n + -48 + -46n

Reorder the terms:
-48 + -46n + 2n2 = 48 + -48 + 46n + -46n

Combine like terms: 48 + -48 = 0
-48 + -46n + 2n2 = 0 + 46n + -46n
-48 + -46n + 2n2 = 46n + -46n

Combine like terms: 46n + -46n = 0
-48 + -46n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -23n + n2) = 0

Factor a trinomial.
2((-1 + -1n)(24 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -1n)' equal to zero and attempt to solve:

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

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

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

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

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

Simplifying
n = -1
Subproblem 2
Set the factor '(24 + -1n)' equal to zero and attempt to solve:

Simplifying
24 + -1n = 0

Solving
24 + -1n = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1n = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1n = 0 + -24
-1n = 0 + -24

Combine like terms: 0 + -24 = -24
-1n = -24

Divide each side by '-1'.
n = 24

Simplifying
n = 24
Solution
n = {-1, 24}