7n^2+16n+15=2n^2+4

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Solution for 7n^2+16n+15=2n^2+4 equation: 


Simplifying
7n2 + 16n + 15 = 2n2 + 4

Reorder the terms:
15 + 16n + 7n2 = 2n2 + 4

Reorder the terms:
15 + 16n + 7n2 = 4 + 2n2

Solving
15 + 16n + 7n2 = 4 + 2n2

Solving for variable 'n'.

Reorder the terms:
15 + -4 + 16n + 7n2 + -2n2 = 4 + 2n2 + -4 + -2n2

Combine like terms: 15 + -4 = 11
11 + 16n + 7n2 + -2n2 = 4 + 2n2 + -4 + -2n2

Combine like terms: 7n2 + -2n2 = 5n2
11 + 16n + 5n2 = 4 + 2n2 + -4 + -2n2

Reorder the terms:
11 + 16n + 5n2 = 4 + -4 + 2n2 + -2n2

Combine like terms: 4 + -4 = 0
11 + 16n + 5n2 = 0 + 2n2 + -2n2
11 + 16n + 5n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
11 + 16n + 5n2 = 0

Factor a trinomial.
(11 + 5n)(1 + n) = 0


Subproblem 1
Set the factor '(11 + 5n)' equal to zero and attempt to solve:

Simplifying
11 + 5n = 0

Solving
11 + 5n = 0

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

Add '-11' to each side of the equation.
11 + -11 + 5n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 5n = 0 + -11
5n = 0 + -11

Combine like terms: 0 + -11 = -11
5n = -11

Divide each side by '5'.
n = -2.2

Simplifying
n = -2.2

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 = {-2.2, -1}

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