3n(n-10)(3n+7)=0

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Solution for 3n(n-10)(3n+7)=0 equation: 


Simplifying
3n(n + -10)(3n + 7) = 0

Reorder the terms:
3n(-10 + n)(3n + 7) = 0

Reorder the terms:
3n(-10 + n)(7 + 3n) = 0

Multiply (-10 + n) * (7 + 3n)
3n(-10(7 + 3n) + n(7 + 3n)) = 0
3n((7 * -10 + 3n * -10) + n(7 + 3n)) = 0
3n((-70 + -30n) + n(7 + 3n)) = 0
3n(-70 + -30n + (7 * n + 3n * n)) = 0
3n(-70 + -30n + (7n + 3n2)) = 0

Combine like terms: -30n + 7n = -23n
3n(-70 + -23n + 3n2) = 0
(-70 * 3n + -23n * 3n + 3n2 * 3n) = 0
(-210n + -69n2 + 9n3) = 0

Solving
-210n + -69n2 + 9n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3n'.
3n(-70 + -23n + 3n2) = 0

Factor a trinomial.
3n((-7 + -3n)(10 + -1n)) = 0

Ignore the factor 3.

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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
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 3
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {0, -2.333333333, 10}

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