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

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


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

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

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

Multiply (-2 + 3n) * (7 + n)
2(-2(7 + n) + 3n * (7 + n)) = 0
2((7 * -2 + n * -2) + 3n * (7 + n)) = 0
2((-14 + -2n) + 3n * (7 + n)) = 0
2(-14 + -2n + (7 * 3n + n * 3n)) = 0
2(-14 + -2n + (21n + 3n2)) = 0

Combine like terms: -2n + 21n = 19n
2(-14 + 19n + 3n2) = 0
(-14 * 2 + 19n * 2 + 3n2 * 2) = 0
(-28 + 38n + 6n2) = 0

Solving
-28 + 38n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 19n + 3n2) = 0

Factor a trinomial.
2((-7 + -1n)(2 + -3n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 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 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7

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

Simplifying
2 + -3n = 0

Solving
2 + -3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3n = 0 + -2
-3n = 0 + -2

Combine like terms: 0 + -2 = -2
-3n = -2

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Solution
n = {-7, 0.6666666667}

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