3n(2n-7)(10n+2)=0

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Solution for 3n(2n-7)(10n+2)=0 equation: 


Simplifying
3n(2n + -7)(10n + 2) = 0

Reorder the terms:
3n(-7 + 2n)(10n + 2) = 0

Reorder the terms:
3n(-7 + 2n)(2 + 10n) = 0

Multiply (-7 + 2n) * (2 + 10n)
3n(-7(2 + 10n) + 2n * (2 + 10n)) = 0
3n((2 * -7 + 10n * -7) + 2n * (2 + 10n)) = 0
3n((-14 + -70n) + 2n * (2 + 10n)) = 0
3n(-14 + -70n + (2 * 2n + 10n * 2n)) = 0
3n(-14 + -70n + (4n + 20n2)) = 0

Combine like terms: -70n + 4n = -66n
3n(-14 + -66n + 20n2) = 0
(-14 * 3n + -66n * 3n + 20n2 * 3n) = 0
(-42n + -198n2 + 60n3) = 0

Solving
-42n + -198n2 + 60n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6n'.
6n(-7 + -33n + 10n2) = 0

Factor a trinomial.
6n((-1 + -5n)(7 + -2n)) = 0

Ignore the factor 6.

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 '(-1 + -5n)' equal to zero and attempt to solve:

Simplifying
-1 + -5n = 0

Solving
-1 + -5n = 0

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

Add '1' to each side of the equation.
-1 + 1 + -5n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5n = 0 + 1
-5n = 0 + 1

Combine like terms: 0 + 1 = 1
-5n = 1

Divide each side by '-5'.
n = -0.2

Simplifying
n = -0.2

Subproblem 3
Set the factor '(7 + -2n)' equal to zero and attempt to solve:

Simplifying
7 + -2n = 0

Solving
7 + -2n = 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 + -2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2n = 0 + -7
-2n = 0 + -7

Combine like terms: 0 + -7 = -7
-2n = -7

Divide each side by '-2'.
n = 3.5

Simplifying
n = 3.5
Solution
n = {0, -0.2, 3.5}

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