3n(n-1)=7(1-n)

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Solution for 3n(n-1)=7(1-n) equation: 


Simplifying
3n(n + -1) = 7(1 + -1n)

Reorder the terms:
3n(-1 + n) = 7(1 + -1n)
(-1 * 3n + n * 3n) = 7(1 + -1n)
(-3n + 3n2) = 7(1 + -1n)
-3n + 3n2 = (1 * 7 + -1n * 7)
-3n + 3n2 = (7 + -7n)

Solving
-3n + 3n2 = 7 + -7n

Solving for variable 'n'.

Reorder the terms:
-7 + -3n + 7n + 3n2 = 7 + -7n + -7 + 7n

Combine like terms: -3n + 7n = 4n
-7 + 4n + 3n2 = 7 + -7n + -7 + 7n

Reorder the terms:
-7 + 4n + 3n2 = 7 + -7 + -7n + 7n

Combine like terms: 7 + -7 = 0
-7 + 4n + 3n2 = 0 + -7n + 7n
-7 + 4n + 3n2 = -7n + 7n

Combine like terms: -7n + 7n = 0
-7 + 4n + 3n2 = 0

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


Subproblem 1
Set the factor '(-7 + -3n)' equal to zero and attempt to solve:

Simplifying
-7 + -3n = 0

Solving
-7 + -3n = 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 + -3n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3n = 0 + 7
-3n = 0 + 7

Combine like terms: 0 + 7 = 7
-3n = 7

Divide each side by '-3'.
n = -2.333333333

Simplifying
n = -2.333333333

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

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

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

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

Simplifying
n = 1
Solution
n = {-2.333333333, 1}

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