(n+7)(11n-2)=18n(2n+1)

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Solution for (n+7)(11n-2)=18n(2n+1) equation:


Simplifying
(n + 7)(11n + -2) = 18n(2n + 1)

Reorder the terms:
(7 + n)(11n + -2) = 18n(2n + 1)

Reorder the terms:
(7 + n)(-2 + 11n) = 18n(2n + 1)

Multiply (7 + n) * (-2 + 11n)
(7(-2 + 11n) + n(-2 + 11n)) = 18n(2n + 1)
((-2 * 7 + 11n * 7) + n(-2 + 11n)) = 18n(2n + 1)
((-14 + 77n) + n(-2 + 11n)) = 18n(2n + 1)
(-14 + 77n + (-2 * n + 11n * n)) = 18n(2n + 1)
(-14 + 77n + (-2n + 11n2)) = 18n(2n + 1)

Combine like terms: 77n + -2n = 75n
(-14 + 75n + 11n2) = 18n(2n + 1)

Reorder the terms:
-14 + 75n + 11n2 = 18n(1 + 2n)
-14 + 75n + 11n2 = (1 * 18n + 2n * 18n)
-14 + 75n + 11n2 = (18n + 36n2)

Solving
-14 + 75n + 11n2 = 18n + 36n2

Solving for variable 'n'.

Reorder the terms:
-14 + 75n + -18n + 11n2 + -36n2 = 18n + 36n2 + -18n + -36n2

Combine like terms: 75n + -18n = 57n
-14 + 57n + 11n2 + -36n2 = 18n + 36n2 + -18n + -36n2

Combine like terms: 11n2 + -36n2 = -25n2
-14 + 57n + -25n2 = 18n + 36n2 + -18n + -36n2

Reorder the terms:
-14 + 57n + -25n2 = 18n + -18n + 36n2 + -36n2

Combine like terms: 18n + -18n = 0
-14 + 57n + -25n2 = 0 + 36n2 + -36n2
-14 + 57n + -25n2 = 36n2 + -36n2

Combine like terms: 36n2 + -36n2 = 0
-14 + 57n + -25n2 = 0

Factor a trinomial.
(-2 + n)(7 + -25n) = 0

Subproblem 1

Set the factor '(-2 + n)' equal to zero and attempt to solve: Simplifying -2 + n = 0 Solving -2 + n = 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 + n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + n = 0 + 2 n = 0 + 2 Combine like terms: 0 + 2 = 2 n = 2 Simplifying n = 2

Subproblem 2

Set the factor '(7 + -25n)' equal to zero and attempt to solve: Simplifying 7 + -25n = 0 Solving 7 + -25n = 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 + -25n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -25n = 0 + -7 -25n = 0 + -7 Combine like terms: 0 + -7 = -7 -25n = -7 Divide each side by '-25'. n = 0.28 Simplifying n = 0.28

Solution

n = {2, 0.28}

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