(6n+7)(7n-1)=0

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Solution for (6n+7)(7n-1)=0 equation:


Simplifying
(6n + 7)(7n + -1) = 0

Reorder the terms:
(7 + 6n)(7n + -1) = 0

Reorder the terms:
(7 + 6n)(-1 + 7n) = 0

Multiply (7 + 6n) * (-1 + 7n)
(7(-1 + 7n) + 6n * (-1 + 7n)) = 0
((-1 * 7 + 7n * 7) + 6n * (-1 + 7n)) = 0
((-7 + 49n) + 6n * (-1 + 7n)) = 0
(-7 + 49n + (-1 * 6n + 7n * 6n)) = 0
(-7 + 49n + (-6n + 42n2)) = 0

Combine like terms: 49n + -6n = 43n
(-7 + 43n + 42n2) = 0

Solving
-7 + 43n + 42n2 = 0

Solving for variable 'n'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(1 + -7n)' equal to zero and attempt to solve:

Simplifying
1 + -7n = 0

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

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

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

Divide each side by '-7'.
n = 0.1428571429

Simplifying
n = 0.1428571429
Solution
n = {-1.166666667, 0.1428571429}

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