14n^2+19n-55=1-n^2

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Solution for 14n^2+19n-55=1-n^2 equation: 


Simplifying
14n2 + 19n + -55 = 1 + -1n2

Reorder the terms:
-55 + 19n + 14n2 = 1 + -1n2

Solving
-55 + 19n + 14n2 = 1 + -1n2

Solving for variable 'n'.

Reorder the terms:
-55 + -1 + 19n + 14n2 + n2 = 1 + -1n2 + -1 + n2

Combine like terms: -55 + -1 = -56
-56 + 19n + 14n2 + n2 = 1 + -1n2 + -1 + n2

Combine like terms: 14n2 + n2 = 15n2
-56 + 19n + 15n2 = 1 + -1n2 + -1 + n2

Reorder the terms:
-56 + 19n + 15n2 = 1 + -1 + -1n2 + n2

Combine like terms: 1 + -1 = 0
-56 + 19n + 15n2 = 0 + -1n2 + n2
-56 + 19n + 15n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-56 + 19n + 15n2 = 0

Factor a trinomial.
(-8 + -3n)(7 + -5n) = 0


Subproblem 1
Set the factor '(-8 + -3n)' equal to zero and attempt to solve:

Simplifying
-8 + -3n = 0

Solving
-8 + -3n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3n = 0 + 8
-3n = 0 + 8

Combine like terms: 0 + 8 = 8
-3n = 8

Divide each side by '-3'.
n = -2.666666667

Simplifying
n = -2.666666667

Subproblem 2
Set the factor '(7 + -5n)' equal to zero and attempt to solve:

Simplifying
7 + -5n = 0

Solving
7 + -5n = 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 + -5n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5n = 0 + -7
-5n = 0 + -7

Combine like terms: 0 + -7 = -7
-5n = -7

Divide each side by '-5'.
n = 1.4

Simplifying
n = 1.4
Solution
n = {-2.666666667, 1.4}

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