(9n+11)(n+9)=79

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Solution for (9n+11)(n+9)=79 equation:


Simplifying
(9n + 11)(n + 9) = 79

Reorder the terms:
(11 + 9n)(n + 9) = 79

Reorder the terms:
(11 + 9n)(9 + n) = 79

Multiply (11 + 9n) * (9 + n)
(11(9 + n) + 9n * (9 + n)) = 79
((9 * 11 + n * 11) + 9n * (9 + n)) = 79
((99 + 11n) + 9n * (9 + n)) = 79
(99 + 11n + (9 * 9n + n * 9n)) = 79
(99 + 11n + (81n + 9n2)) = 79

Combine like terms: 11n + 81n = 92n
(99 + 92n + 9n2) = 79

Solving
99 + 92n + 9n2 = 79

Solving for variable 'n'.

Reorder the terms:
99 + -79 + 92n + 9n2 = 79 + -79

Combine like terms: 99 + -79 = 20
20 + 92n + 9n2 = 79 + -79

Combine like terms: 79 + -79 = 0
20 + 92n + 9n2 = 0

Factor a trinomial.
(10 + n)(2 + 9n) = 0

Subproblem 1

Set the factor '(10 + n)' equal to zero and attempt to solve: Simplifying 10 + n = 0 Solving 10 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + n = 0 + -10 n = 0 + -10 Combine like terms: 0 + -10 = -10 n = -10 Simplifying n = -10

Subproblem 2

Set the factor '(2 + 9n)' equal to zero and attempt to solve: Simplifying 2 + 9n = 0 Solving 2 + 9n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 9n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9n = 0 + -2 9n = 0 + -2 Combine like terms: 0 + -2 = -2 9n = -2 Divide each side by '9'. n = -0.2222222222 Simplifying n = -0.2222222222

Solution

n = {-10, -0.2222222222}

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