15300=2(2n-1)(n-6)(n-10)

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Solution for 15300=2(2n-1)(n-6)(n-10) equation: 


Simplifying
15300 = 2(2n + -1)(n + -6)(n + -10)

Reorder the terms:
15300 = 2(-1 + 2n)(n + -6)(n + -10)

Reorder the terms:
15300 = 2(-1 + 2n)(-6 + n)(n + -10)

Reorder the terms:
15300 = 2(-1 + 2n)(-6 + n)(-10 + n)

Multiply (-1 + 2n) * (-6 + n)
15300 = 2(-1(-6 + n) + 2n * (-6 + n))(-10 + n)
15300 = 2((-6 * -1 + n * -1) + 2n * (-6 + n))(-10 + n)
15300 = 2((6 + -1n) + 2n * (-6 + n))(-10 + n)
15300 = 2(6 + -1n + (-6 * 2n + n * 2n))(-10 + n)
15300 = 2(6 + -1n + (-12n + 2n2))(-10 + n)

Combine like terms: -1n + -12n = -13n
15300 = 2(6 + -13n + 2n2)(-10 + n)

Multiply (6 + -13n + 2n2) * (-10 + n)
15300 = 2(6(-10 + n) + -13n * (-10 + n) + 2n2 * (-10 + n))
15300 = 2((-10 * 6 + n * 6) + -13n * (-10 + n) + 2n2 * (-10 + n))
15300 = 2((-60 + 6n) + -13n * (-10 + n) + 2n2 * (-10 + n))
15300 = 2(-60 + 6n + (-10 * -13n + n * -13n) + 2n2 * (-10 + n))
15300 = 2(-60 + 6n + (130n + -13n2) + 2n2 * (-10 + n))
15300 = 2(-60 + 6n + 130n + -13n2 + (-10 * 2n2 + n * 2n2))
15300 = 2(-60 + 6n + 130n + -13n2 + (-20n2 + 2n3))

Combine like terms: 6n + 130n = 136n
15300 = 2(-60 + 136n + -13n2 + -20n2 + 2n3)

Combine like terms: -13n2 + -20n2 = -33n2
15300 = 2(-60 + 136n + -33n2 + 2n3)
15300 = (-60 * 2 + 136n * 2 + -33n2 * 2 + 2n3 * 2)
15300 = (-120 + 272n + -66n2 + 4n3)

Solving
15300 = -120 + 272n + -66n2 + 4n3

Solving for variable 'n'.

Combine like terms: 15300 + 120 = 15420
15420 + -272n + 66n2 + -4n3 = -120 + 272n + -66n2 + 4n3 + 120 + -272n + 66n2 + -4n3

Reorder the terms:
15420 + -272n + 66n2 + -4n3 = -120 + 120 + 272n + -272n + -66n2 + 66n2 + 4n3 + -4n3

Combine like terms: -120 + 120 = 0
15420 + -272n + 66n2 + -4n3 = 0 + 272n + -272n + -66n2 + 66n2 + 4n3 + -4n3
15420 + -272n + 66n2 + -4n3 = 272n + -272n + -66n2 + 66n2 + 4n3 + -4n3

Combine like terms: 272n + -272n = 0
15420 + -272n + 66n2 + -4n3 = 0 + -66n2 + 66n2 + 4n3 + -4n3
15420 + -272n + 66n2 + -4n3 = -66n2 + 66n2 + 4n3 + -4n3

Combine like terms: -66n2 + 66n2 = 0
15420 + -272n + 66n2 + -4n3 = 0 + 4n3 + -4n3
15420 + -272n + 66n2 + -4n3 = 4n3 + -4n3

Combine like terms: 4n3 + -4n3 = 0
15420 + -272n + 66n2 + -4n3 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7710 + -136n + 33n2 + -2n3) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7710 + -136n + 33n2 + -2n3)' equal to zero and attempt to solve:

Simplifying
7710 + -136n + 33n2 + -2n3 = 0

Solving
7710 + -136n + 33n2 + -2n3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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