(N-4)(n-5)(n-6)=210

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Solution for (N-4)(n-5)(n-6)=210 equation: 


Simplifying
(N + -4)(n + -5)(n + -6) = 210

Reorder the terms:
(-4 + N)(n + -5)(n + -6) = 210

Reorder the terms:
(-4 + N)(-5 + n)(n + -6) = 210

Reorder the terms:
(-4 + N)(-5 + n)(-6 + n) = 210

Multiply (-4 + N) * (-5 + n)
(-4(-5 + n) + N(-5 + n))(-6 + n) = 210
((-5 * -4 + n * -4) + N(-5 + n))(-6 + n) = 210
((20 + -4n) + N(-5 + n))(-6 + n) = 210
(20 + -4n + (-5 * N + n * N))(-6 + n) = 210
(20 + -4n + (-5N + nN))(-6 + n) = 210

Reorder the terms:
(20 + -5N + -4n + nN)(-6 + n) = 210
(20 + -5N + -4n + nN)(-6 + n) = 210

Multiply (20 + -5N + -4n + nN) * (-6 + n)
(20(-6 + n) + -5N * (-6 + n) + -4n * (-6 + n) + nN(-6 + n)) = 210
((-6 * 20 + n * 20) + -5N * (-6 + n) + -4n * (-6 + n) + nN(-6 + n)) = 210
((-120 + 20n) + -5N * (-6 + n) + -4n * (-6 + n) + nN(-6 + n)) = 210
(-120 + 20n + (-6 * -5N + n * -5N) + -4n * (-6 + n) + nN(-6 + n)) = 210
(-120 + 20n + (30N + -5nN) + -4n * (-6 + n) + nN(-6 + n)) = 210
(-120 + 20n + 30N + -5nN + (-6 * -4n + n * -4n) + nN(-6 + n)) = 210
(-120 + 20n + 30N + -5nN + (24n + -4n2) + nN(-6 + n)) = 210
(-120 + 20n + 30N + -5nN + 24n + -4n2 + (-6 * nN + n * nN)) = 210
(-120 + 20n + 30N + -5nN + 24n + -4n2 + (-6nN + n2N)) = 210

Reorder the terms:
(-120 + 30N + 20n + 24n + -5nN + -6nN + -4n2 + n2N) = 210

Combine like terms: 20n + 24n = 44n
(-120 + 30N + 44n + -5nN + -6nN + -4n2 + n2N) = 210

Combine like terms: -5nN + -6nN = -11nN
(-120 + 30N + 44n + -11nN + -4n2 + n2N) = 210

Solving
-120 + 30N + 44n + -11nN + -4n2 + n2N = 210

Solving for variable 'N'.

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

Add '120' to each side of the equation.
-120 + 30N + 44n + -11nN + -4n2 + 120 + n2N = 210 + 120

Reorder the terms:
-120 + 120 + 30N + 44n + -11nN + -4n2 + n2N = 210 + 120

Combine like terms: -120 + 120 = 0
0 + 30N + 44n + -11nN + -4n2 + n2N = 210 + 120
30N + 44n + -11nN + -4n2 + n2N = 210 + 120

Combine like terms: 210 + 120 = 330
30N + 44n + -11nN + -4n2 + n2N = 330

Add '-44n' to each side of the equation.
30N + 44n + -11nN + -4n2 + -44n + n2N = 330 + -44n

Reorder the terms:
30N + 44n + -44n + -11nN + -4n2 + n2N = 330 + -44n

Combine like terms: 44n + -44n = 0
30N + 0 + -11nN + -4n2 + n2N = 330 + -44n
30N + -11nN + -4n2 + n2N = 330 + -44n

Add '4n2' to each side of the equation.
30N + -11nN + -4n2 + 4n2 + n2N = 330 + -44n + 4n2

Combine like terms: -4n2 + 4n2 = 0
30N + -11nN + 0 + n2N = 330 + -44n + 4n2
30N + -11nN + n2N = 330 + -44n + 4n2

Reorder the terms:
-330 + 30N + 44n + -11nN + -4n2 + n2N = 330 + -44n + 4n2 + -330 + 44n + -4n2

Reorder the terms:
-330 + 30N + 44n + -11nN + -4n2 + n2N = 330 + -330 + -44n + 44n + 4n2 + -4n2

Combine like terms: 330 + -330 = 0
-330 + 30N + 44n + -11nN + -4n2 + n2N = 0 + -44n + 44n + 4n2 + -4n2
-330 + 30N + 44n + -11nN + -4n2 + n2N = -44n + 44n + 4n2 + -4n2

Combine like terms: -44n + 44n = 0
-330 + 30N + 44n + -11nN + -4n2 + n2N = 0 + 4n2 + -4n2
-330 + 30N + 44n + -11nN + -4n2 + n2N = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
-330 + 30N + 44n + -11nN + -4n2 + n2N = 0

The solution to this equation could not be determined.

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