=(6mp+30np)(-2m-10n)

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Solution for =(6mp+30np)(-2m-10n) equation: 


Simplifying
0 = (6mp + 30np)(-2m + -10n)

Multiply (6mp + 30np) * (-2m + -10n)
0 = (6mp * (-2m + -10n) + 30np * (-2m + -10n))
0 = ((-2m * 6mp + -10n * 6mp) + 30np * (-2m + -10n))

Reorder the terms:
0 = ((-60mnp + -12m2p) + 30np * (-2m + -10n))
0 = ((-60mnp + -12m2p) + 30np * (-2m + -10n))
0 = (-60mnp + -12m2p + (-2m * 30np + -10n * 30np))
0 = (-60mnp + -12m2p + (-60mnp + -300n2p))

Reorder the terms:
0 = (-60mnp + -60mnp + -12m2p + -300n2p)

Combine like terms: -60mnp + -60mnp = -120mnp
0 = (-120mnp + -12m2p + -300n2p)

Solving
0 = -120mnp + -12m2p + -300n2p

Solving for variable 'm'.
Remove the zero:
120mnp + 12m2p + 300n2p = -120mnp + -12m2p + -300n2p + 120mnp + 12m2p + 300n2p

Reorder the terms:
120mnp + 12m2p + 300n2p = -120mnp + 120mnp + -12m2p + 12m2p + -300n2p + 300n2p

Combine like terms: -120mnp + 120mnp = 0
120mnp + 12m2p + 300n2p = 0 + -12m2p + 12m2p + -300n2p + 300n2p
120mnp + 12m2p + 300n2p = -12m2p + 12m2p + -300n2p + 300n2p

Combine like terms: -12m2p + 12m2p = 0
120mnp + 12m2p + 300n2p = 0 + -300n2p + 300n2p
120mnp + 12m2p + 300n2p = -300n2p + 300n2p

Combine like terms: -300n2p + 300n2p = 0
120mnp + 12m2p + 300n2p = 0

Factor out the Greatest Common Factor (GCF), '12p'.
12p(10mn + m2 + 25n2) = 0

Factor a trinomial.
12p((m + 5n)(m + 5n)) = 0

Ignore the factor 12.

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

Simplifying
p = 0

Solving
p = 0

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

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

Simplifying
0 = -1p

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 '(m + 5n)' equal to zero and attempt to solve:

Simplifying
m + 5n = 0

Solving
m + 5n = 0

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

Add '-5n' to each side of the equation.
m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
m + 0 = 0 + -5n
m = 0 + -5n
Remove the zero:
m = -5n

Simplifying
m = -5n

Subproblem 3
Set the factor '(m + 5n)' equal to zero and attempt to solve:

Simplifying
m + 5n = 0

Solving
m + 5n = 0

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

Add '-5n' to each side of the equation.
m + 5n + -5n = 0 + -5n

Combine like terms: 5n + -5n = 0
m + 0 = 0 + -5n
m = 0 + -5n
Remove the zero:
m = -5n

Simplifying
m = -5n
Solution
m = {-5n, -5n}

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