(2n+7)(6n+7)=0

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Solution for (2n+7)(6n+7)=0 equation: 


Simplifying
(2n + 7)(6n + 7) = 0

Reorder the terms:
(7 + 2n)(6n + 7) = 0

Reorder the terms:
(7 + 2n)(7 + 6n) = 0

Multiply (7 + 2n) * (7 + 6n)
(7(7 + 6n) + 2n * (7 + 6n)) = 0
((7 * 7 + 6n * 7) + 2n * (7 + 6n)) = 0
((49 + 42n) + 2n * (7 + 6n)) = 0
(49 + 42n + (7 * 2n + 6n * 2n)) = 0
(49 + 42n + (14n + 12n2)) = 0

Combine like terms: 42n + 14n = 56n
(49 + 56n + 12n2) = 0

Solving
49 + 56n + 12n2 = 0

Solving for variable 'n'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(7 + 6n)' equal to zero and attempt to solve:

Simplifying
7 + 6n = 0

Solving
7 + 6n = 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 + 6n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6n = 0 + -7
6n = 0 + -7

Combine like terms: 0 + -7 = -7
6n = -7

Divide each side by '6'.
n = -1.166666667

Simplifying
n = -1.166666667
Solution
n = {-3.5, -1.166666667}

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