2n^2-49=-7n

Solution for 2n^2-49=-7n equation:

Simplifying
2n2 + -49 = -7n

Reorder the terms:
-49 + 2n2 = -7n

Solving
-49 + 2n2 = -7n

Solving for variable 'n'.

Reorder the terms:
-49 + 7n + 2n2 = -7n + 7n

Combine like terms: -7n + 7n = 0
-49 + 7n + 2n2 = 0

Factor a trinomial.
(-7 + -1n)(7 + -2n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(7 + -2n)' equal to zero and attempt to solve:

Simplifying
7 + -2n = 0

Solving
7 + -2n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2n = 0 + -7
-2n = 0 + -7

Combine like terms: 0 + -7 = -7
-2n = -7

Divide each side by '-2'.
n = 3.5

Simplifying
n = 3.5
Solution
n = {-7, 3.5}