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

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


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

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

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

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

Combine like terms: 42n + 1n = 43n
(7 + 43n + 6n2) = 0

Solving
7 + 43n + 6n2 = 0

Solving for variable 'n'.

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

Subproblem 1

Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 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 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7

Subproblem 2

Set the factor '(1 + 6n)' equal to zero and attempt to solve: Simplifying 1 + 6n = 0 Solving 1 + 6n = 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 + 6n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6n = 0 + -1 6n = 0 + -1 Combine like terms: 0 + -1 = -1 6n = -1 Divide each side by '6'. n = -0.1666666667 Simplifying n = -0.1666666667

Solution

n = {-7, -0.1666666667}

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