-2n^2+9=-7n

Solution for -2n^2+9=-7n equation:

Simplifying
-2n2 + 9 = -7n

Reorder the terms:
9 + -2n2 = -7n

Solving
9 + -2n2 = -7n

Solving for variable 'n'.

Reorder the terms:
9 + 7n + -2n2 = -7n + 7n

Combine like terms: -7n + 7n = 0
9 + 7n + -2n2 = 0

Factor a trinomial.
(9 + -2n)(1 + n) = 0

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

Simplifying
1 + n = 0

Solving
1 + n = 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 + n = 0 + -1

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

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

Simplifying
n = -1
Solution
n = {4.5, -1}