21cm^2=(n+3cm)(m-8cm)

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Solution for 21cm^2=(n+3cm)(m-8cm) equation: 


Simplifying
21cm2 = (n + 3cm)(m + -8cm)

Reorder the terms:
21cm2 = (3cm + n)(m + -8cm)

Reorder the terms:
21cm2 = (3cm + n)(-8cm + m)

Multiply (3cm + n) * (-8cm + m)
21cm2 = (3cm * (-8cm + m) + n(-8cm + m))
21cm2 = ((-8cm * 3cm + m * 3cm) + n(-8cm + m))

Reorder the terms:
21cm2 = ((3cm2 + -24c2m2) + n(-8cm + m))
21cm2 = ((3cm2 + -24c2m2) + n(-8cm + m))
21cm2 = (3cm2 + -24c2m2 + (-8cm * n + m * n))
21cm2 = (3cm2 + -24c2m2 + (-8cmn + mn))

Reorder the terms:
21cm2 = (-8cmn + 3cm2 + -24c2m2 + mn)
21cm2 = (-8cmn + 3cm2 + -24c2m2 + mn)

Solving
21cm2 = -8cmn + 3cm2 + -24c2m2 + mn

Solving for variable 'c'.

Reorder the terms:
8cmn + 21cm2 + -3cm2 + 24c2m2 + -1mn = -8cmn + 3cm2 + -24c2m2 + mn + 8cmn + -3cm2 + 24c2m2 + -1mn

Combine like terms: 21cm2 + -3cm2 = 18cm2
8cmn + 18cm2 + 24c2m2 + -1mn = -8cmn + 3cm2 + -24c2m2 + mn + 8cmn + -3cm2 + 24c2m2 + -1mn

Reorder the terms:
8cmn + 18cm2 + 24c2m2 + -1mn = -8cmn + 8cmn + 3cm2 + -3cm2 + -24c2m2 + 24c2m2 + mn + -1mn

Combine like terms: -8cmn + 8cmn = 0
8cmn + 18cm2 + 24c2m2 + -1mn = 0 + 3cm2 + -3cm2 + -24c2m2 + 24c2m2 + mn + -1mn
8cmn + 18cm2 + 24c2m2 + -1mn = 3cm2 + -3cm2 + -24c2m2 + 24c2m2 + mn + -1mn

Combine like terms: 3cm2 + -3cm2 = 0
8cmn + 18cm2 + 24c2m2 + -1mn = 0 + -24c2m2 + 24c2m2 + mn + -1mn
8cmn + 18cm2 + 24c2m2 + -1mn = -24c2m2 + 24c2m2 + mn + -1mn

Combine like terms: -24c2m2 + 24c2m2 = 0
8cmn + 18cm2 + 24c2m2 + -1mn = 0 + mn + -1mn
8cmn + 18cm2 + 24c2m2 + -1mn = mn + -1mn

Combine like terms: mn + -1mn = 0
8cmn + 18cm2 + 24c2m2 + -1mn = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(8cn + 18cm + 24c2m + -1n) = 0


Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Add '-1m' to each side of the equation.
m + -1m = 0 + -1m
Remove the zero:
0 = -1m

Simplifying
0 = -1m

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(8cn + 18cm + 24c2m + -1n)' equal to zero and attempt to solve:

Simplifying
8cn + 18cm + 24c2m + -1n = 0

Reorder the terms:
18cm + 8cn + 24c2m + -1n = 0

Solving
18cm + 8cn + 24c2m + -1n = 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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