-5n^2+27n-14=8n-8n^2

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Solution for -5n^2+27n-14=8n-8n^2 equation: 


Simplifying
-5n2 + 27n + -14 = 8n + -8n2

Reorder the terms:
-14 + 27n + -5n2 = 8n + -8n2

Solving
-14 + 27n + -5n2 = 8n + -8n2

Solving for variable 'n'.

Reorder the terms:
-14 + 27n + -8n + -5n2 + 8n2 = 8n + -8n2 + -8n + 8n2

Combine like terms: 27n + -8n = 19n
-14 + 19n + -5n2 + 8n2 = 8n + -8n2 + -8n + 8n2

Combine like terms: -5n2 + 8n2 = 3n2
-14 + 19n + 3n2 = 8n + -8n2 + -8n + 8n2

Reorder the terms:
-14 + 19n + 3n2 = 8n + -8n + -8n2 + 8n2

Combine like terms: 8n + -8n = 0
-14 + 19n + 3n2 = 0 + -8n2 + 8n2
-14 + 19n + 3n2 = -8n2 + 8n2

Combine like terms: -8n2 + 8n2 = 0
-14 + 19n + 3n2 = 0

Factor a trinomial.
(-7 + -1n)(2 + -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 '(2 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

Solving
2 + -3n = 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 + -3n = 0 + -2

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

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

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Solution
n = {-7, 0.6666666667}

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