7n^2+16n+15=2n^2+3

Solution for 7n^2+16n+15=2n^2+3 equation:

Simplifying
7n2 + 16n + 15 = 2n2 + 3

Reorder the terms:
15 + 16n + 7n2 = 2n2 + 3

Reorder the terms:
15 + 16n + 7n2 = 3 + 2n2

Solving
15 + 16n + 7n2 = 3 + 2n2

Solving for variable 'n'.

Reorder the terms:
15 + -3 + 16n + 7n2 + -2n2 = 3 + 2n2 + -3 + -2n2

Combine like terms: 15 + -3 = 12
12 + 16n + 7n2 + -2n2 = 3 + 2n2 + -3 + -2n2

Combine like terms: 7n2 + -2n2 = 5n2
12 + 16n + 5n2 = 3 + 2n2 + -3 + -2n2

Reorder the terms:
12 + 16n + 5n2 = 3 + -3 + 2n2 + -2n2

Combine like terms: 3 + -3 = 0
12 + 16n + 5n2 = 0 + 2n2 + -2n2
12 + 16n + 5n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
12 + 16n + 5n2 = 0

Factor a trinomial.
(2 + n)(6 + 5n) = 0

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

Simplifying
2 + n = 0

Solving
2 + n = 0

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

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

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

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

Simplifying
n = -2
Subproblem 2
Set the factor '(6 + 5n)' equal to zero and attempt to solve:

Simplifying
6 + 5n = 0

Solving
6 + 5n = 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 + 5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5n = 0 + -6
5n = 0 + -6

Combine like terms: 0 + -6 = -6
5n = -6

Divide each side by '5'.
n = -1.2

Simplifying
n = -1.2
Solution
n = {-2, -1.2}