(n+6n-4)(2n-4)=0

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Solution for (n+6n-4)(2n-4)=0 equation: 


Simplifying
(n + 6n + -4)(2n + -4) = 0

Reorder the terms:
(-4 + n + 6n)(2n + -4) = 0

Combine like terms: n + 6n = 7n
(-4 + 7n)(2n + -4) = 0

Reorder the terms:
(-4 + 7n)(-4 + 2n) = 0

Multiply (-4 + 7n) * (-4 + 2n)
(-4(-4 + 2n) + 7n * (-4 + 2n)) = 0
((-4 * -4 + 2n * -4) + 7n * (-4 + 2n)) = 0
((16 + -8n) + 7n * (-4 + 2n)) = 0
(16 + -8n + (-4 * 7n + 2n * 7n)) = 0
(16 + -8n + (-28n + 14n2)) = 0

Combine like terms: -8n + -28n = -36n
(16 + -36n + 14n2) = 0

Solving
16 + -36n + 14n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -18n + 7n2) = 0

Factor a trinomial.
2((4 + -7n)(2 + -1n)) = 0

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {0.5714285714, 2}

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