13n^2+16n=16-8n^2

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Solution for 13n^2+16n=16-8n^2 equation: 


Simplifying
13n2 + 16n = 16 + -8n2

Reorder the terms:
16n + 13n2 = 16 + -8n2

Solving
16n + 13n2 = 16 + -8n2

Solving for variable 'n'.

Reorder the terms:
-16 + 16n + 13n2 + 8n2 = 16 + -8n2 + -16 + 8n2

Combine like terms: 13n2 + 8n2 = 21n2
-16 + 16n + 21n2 = 16 + -8n2 + -16 + 8n2

Reorder the terms:
-16 + 16n + 21n2 = 16 + -16 + -8n2 + 8n2

Combine like terms: 16 + -16 = 0
-16 + 16n + 21n2 = 0 + -8n2 + 8n2
-16 + 16n + 21n2 = -8n2 + 8n2

Combine like terms: -8n2 + 8n2 = 0
-16 + 16n + 21n2 = 0

Factor a trinomial.
(-4 + -3n)(4 + -7n) = 0


Subproblem 1
Set the factor '(-4 + -3n)' equal to zero and attempt to solve:

Simplifying
-4 + -3n = 0

Solving
-4 + -3n = 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 + -3n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3n = 0 + 4
-3n = 0 + 4

Combine like terms: 0 + 4 = 4
-3n = 4

Divide each side by '-3'.
n = -1.333333333

Simplifying
n = -1.333333333

Subproblem 2
Set the factor '(4 + -7n)' equal to zero and attempt to solve:

Simplifying
4 + -7n = 0

Solving
4 + -7n = 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 + -7n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7n = 0 + -4
-7n = 0 + -4

Combine like terms: 0 + -4 = -4
-7n = -4

Divide each side by '-7'.
n = 0.5714285714

Simplifying
n = 0.5714285714
Solution
n = {-1.333333333, 0.5714285714}

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