5n^2-77=n^2+8n

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Solution for 5n^2-77=n^2+8n equation: 


Simplifying
5n2 + -77 = n2 + 8n

Reorder the terms:
-77 + 5n2 = n2 + 8n

Reorder the terms:
-77 + 5n2 = 8n + n2

Solving
-77 + 5n2 = 8n + n2

Solving for variable 'n'.

Reorder the terms:
-77 + -8n + 5n2 + -1n2 = 8n + n2 + -8n + -1n2

Combine like terms: 5n2 + -1n2 = 4n2
-77 + -8n + 4n2 = 8n + n2 + -8n + -1n2

Reorder the terms:
-77 + -8n + 4n2 = 8n + -8n + n2 + -1n2

Combine like terms: 8n + -8n = 0
-77 + -8n + 4n2 = 0 + n2 + -1n2
-77 + -8n + 4n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-77 + -8n + 4n2 = 0

Factor a trinomial.
(-7 + -2n)(11 + -2n) = 0


Subproblem 1
Set the factor '(-7 + -2n)' equal to zero and attempt to solve:

Simplifying
-7 + -2n = 0

Solving
-7 + -2n = 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 + -2n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2n = 0 + 7
-2n = 0 + 7

Combine like terms: 0 + 7 = 7
-2n = 7

Divide each side by '-2'.
n = -3.5

Simplifying
n = -3.5

Subproblem 2
Set the factor '(11 + -2n)' equal to zero and attempt to solve:

Simplifying
11 + -2n = 0

Solving
11 + -2n = 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 + -2n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2n = 0 + -11
-2n = 0 + -11

Combine like terms: 0 + -11 = -11
-2n = -11

Divide each side by '-2'.
n = 5.5

Simplifying
n = 5.5
Solution
n = {-3.5, 5.5}

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