-n^2+16n-34=-4n^2+1

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Solution for -n^2+16n-34=-4n^2+1 equation: 


Simplifying
-1n2 + 16n + -34 = -4n2 + 1

Reorder the terms:
-34 + 16n + -1n2 = -4n2 + 1

Reorder the terms:
-34 + 16n + -1n2 = 1 + -4n2

Solving
-34 + 16n + -1n2 = 1 + -4n2

Solving for variable 'n'.

Reorder the terms:
-34 + -1 + 16n + -1n2 + 4n2 = 1 + -4n2 + -1 + 4n2

Combine like terms: -34 + -1 = -35
-35 + 16n + -1n2 + 4n2 = 1 + -4n2 + -1 + 4n2

Combine like terms: -1n2 + 4n2 = 3n2
-35 + 16n + 3n2 = 1 + -4n2 + -1 + 4n2

Reorder the terms:
-35 + 16n + 3n2 = 1 + -1 + -4n2 + 4n2

Combine like terms: 1 + -1 = 0
-35 + 16n + 3n2 = 0 + -4n2 + 4n2
-35 + 16n + 3n2 = -4n2 + 4n2

Combine like terms: -4n2 + 4n2 = 0
-35 + 16n + 3n2 = 0

Factor a trinomial.
(-7 + -1n)(5 + -3n) = 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 '(5 + -3n)' equal to zero and attempt to solve:

Simplifying
5 + -3n = 0

Solving
5 + -3n = 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 + -3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n = 0 + -5
-3n = 0 + -5

Combine like terms: 0 + -5 = -5
-3n = -5

Divide each side by '-3'.
n = 1.666666667

Simplifying
n = 1.666666667
Solution
n = {-7, 1.666666667}

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