2n^2-15=7n

Solution for 2n^2-15=7n equation:

Simplifying
2n2 + -15 = 7n

Reorder the terms:
-15 + 2n2 = 7n

Solving
-15 + 2n2 = 7n

Solving for variable 'n'.

Reorder the terms:
-15 + -7n + 2n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
-15 + -7n + 2n2 = 0

Factor a trinomial.
(-3 + -2n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -2n)' equal to zero and attempt to solve:

Simplifying
-3 + -2n = 0

Solving
-3 + -2n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2n = 0 + 3

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

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

Divide each side by '-2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-1.5, 5}