8n^2-21n-128=-5n-4n^2

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Solution for 8n^2-21n-128=-5n-4n^2 equation: 


Simplifying
8n2 + -21n + -128 = -5n + -4n2

Reorder the terms:
-128 + -21n + 8n2 = -5n + -4n2

Solving
-128 + -21n + 8n2 = -5n + -4n2

Solving for variable 'n'.

Reorder the terms:
-128 + -21n + 5n + 8n2 + 4n2 = -5n + -4n2 + 5n + 4n2

Combine like terms: -21n + 5n = -16n
-128 + -16n + 8n2 + 4n2 = -5n + -4n2 + 5n + 4n2

Combine like terms: 8n2 + 4n2 = 12n2
-128 + -16n + 12n2 = -5n + -4n2 + 5n + 4n2

Reorder the terms:
-128 + -16n + 12n2 = -5n + 5n + -4n2 + 4n2

Combine like terms: -5n + 5n = 0
-128 + -16n + 12n2 = 0 + -4n2 + 4n2
-128 + -16n + 12n2 = -4n2 + 4n2

Combine like terms: -4n2 + 4n2 = 0
-128 + -16n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-32 + -4n + 3n2) = 0

Factor a trinomial.
4((-8 + -3n)(4 + -1n)) = 0

Ignore the factor 4.

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 '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-2.666666667, 4}

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