0=4(n-4)-6n(n-4)

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Solution for 0=4(n-4)-6n(n-4) equation: 


Simplifying
0 = 4(n + -4) + -6n(n + -4)

Reorder the terms:
0 = 4(-4 + n) + -6n(n + -4)
0 = (-4 * 4 + n * 4) + -6n(n + -4)
0 = (-16 + 4n) + -6n(n + -4)

Reorder the terms:
0 = -16 + 4n + -6n(-4 + n)
0 = -16 + 4n + (-4 * -6n + n * -6n)
0 = -16 + 4n + (24n + -6n2)

Combine like terms: 4n + 24n = 28n
0 = -16 + 28n + -6n2

Solving
0 = -16 + 28n + -6n2

Solving for variable 'n'.

Combine like terms: 0 + 16 = 16
16 + -28n + 6n2 = -16 + 28n + -6n2 + 16 + -28n + 6n2

Reorder the terms:
16 + -28n + 6n2 = -16 + 16 + 28n + -28n + -6n2 + 6n2

Combine like terms: -16 + 16 = 0
16 + -28n + 6n2 = 0 + 28n + -28n + -6n2 + 6n2
16 + -28n + 6n2 = 28n + -28n + -6n2 + 6n2

Combine like terms: 28n + -28n = 0
16 + -28n + 6n2 = 0 + -6n2 + 6n2
16 + -28n + 6n2 = -6n2 + 6n2

Combine like terms: -6n2 + 6n2 = 0
16 + -28n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -14n + 3n2) = 0

Factor a trinomial.
2((2 + -3n)(4 + -1n)) = 0

Ignore the factor 2.

Subproblem 1
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

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 = {0.6666666667, 4}

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