(n-11)(3n+7)=0

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Solution for (n-11)(3n+7)=0 equation: 


Simplifying
(n + -11)(3n + 7) = 0

Reorder the terms:
(-11 + n)(3n + 7) = 0

Reorder the terms:
(-11 + n)(7 + 3n) = 0

Multiply (-11 + n) * (7 + 3n)
(-11(7 + 3n) + n(7 + 3n)) = 0
((7 * -11 + 3n * -11) + n(7 + 3n)) = 0
((-77 + -33n) + n(7 + 3n)) = 0
(-77 + -33n + (7 * n + 3n * n)) = 0
(-77 + -33n + (7n + 3n2)) = 0

Combine like terms: -33n + 7n = -26n
(-77 + -26n + 3n2) = 0

Solving
-77 + -26n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-7 + -3n)(11 + -1n) = 0


Subproblem 1
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 2
Set the factor '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 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 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Solution
n = {-2.333333333, 11}

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