7(4n-7)(7n-4)=0

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Solution for 7(4n-7)(7n-4)=0 equation: 


Simplifying
7(4n + -7)(7n + -4) = 0

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

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

Multiply (-7 + 4n) * (-4 + 7n)
7(-7(-4 + 7n) + 4n * (-4 + 7n)) = 0
7((-4 * -7 + 7n * -7) + 4n * (-4 + 7n)) = 0
7((28 + -49n) + 4n * (-4 + 7n)) = 0
7(28 + -49n + (-4 * 4n + 7n * 4n)) = 0
7(28 + -49n + (-16n + 28n2)) = 0

Combine like terms: -49n + -16n = -65n
7(28 + -65n + 28n2) = 0
(28 * 7 + -65n * 7 + 28n2 * 7) = 0
(196 + -455n + 196n2) = 0

Solving
196 + -455n + 196n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '7'.
7(28 + -65n + 28n2) = 0

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

Ignore the factor 7.

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 '(7 + -4n)' equal to zero and attempt to solve:

Simplifying
7 + -4n = 0

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

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

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

Divide each side by '-4'.
n = 1.75

Simplifying
n = 1.75
Solution
n = {0.5714285714, 1.75}

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