(3n+11)(2n-10)=0

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Solution for (3n+11)(2n-10)=0 equation: 


Simplifying
(3n + 11)(2n + -10) = 0

Reorder the terms:
(11 + 3n)(2n + -10) = 0

Reorder the terms:
(11 + 3n)(-10 + 2n) = 0

Multiply (11 + 3n) * (-10 + 2n)
(11(-10 + 2n) + 3n * (-10 + 2n)) = 0
((-10 * 11 + 2n * 11) + 3n * (-10 + 2n)) = 0
((-110 + 22n) + 3n * (-10 + 2n)) = 0
(-110 + 22n + (-10 * 3n + 2n * 3n)) = 0
(-110 + 22n + (-30n + 6n2)) = 0

Combine like terms: 22n + -30n = -8n
(-110 + -8n + 6n2) = 0

Solving
-110 + -8n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + -4n + 3n2) = 0

Factor a trinomial.
2((-11 + -3n)(5 + -1n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + -3n)' equal to zero and attempt to solve:

Simplifying
-11 + -3n = 0

Solving
-11 + -3n = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3n = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3n = 0 + 11
-3n = 0 + 11

Combine like terms: 0 + 11 = 11
-3n = 11

Divide each side by '-3'.
n = -3.666666667

Simplifying
n = -3.666666667

Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

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

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

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

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-3.666666667, 5}

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