(n-7)(3n-2)=0

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Solution for (n-7)(3n-2)=0 equation: 


Simplifying
(n + -7)(3n + -2) = 0

Reorder the terms:
(-7 + n)(3n + -2) = 0

Reorder the terms:
(-7 + n)(-2 + 3n) = 0

Multiply (-7 + n) * (-2 + 3n)
(-7(-2 + 3n) + n(-2 + 3n)) = 0
((-2 * -7 + 3n * -7) + n(-2 + 3n)) = 0
((14 + -21n) + n(-2 + 3n)) = 0
(14 + -21n + (-2 * n + 3n * n)) = 0
(14 + -21n + (-2n + 3n2)) = 0

Combine like terms: -21n + -2n = -23n
(14 + -23n + 3n2) = 0

Solving
14 + -23n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(2 + -3n)(7 + -1n) = 0


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 '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {0.6666666667, 7}

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