6(n+75)9n=1725

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Solution for 6(n+75)9n=1725 equation:


Simplifying
6(n + 75) * 9n = 1725

Reorder the terms:
6(75 + n) * 9n = 1725

Reorder the terms for easier multiplication:
6 * 9n(75 + n) = 1725

Multiply 6 * 9
54n(75 + n) = 1725
(75 * 54n + n * 54n) = 1725
(4050n + 54n2) = 1725

Solving
4050n + 54n2 = 1725

Solving for variable 'n'.

Reorder the terms:
-1725 + 4050n + 54n2 = 1725 + -1725

Combine like terms: 1725 + -1725 = 0
-1725 + 4050n + 54n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-575 + 1350n + 18n2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-575 + 1350n + 18n2)' equal to zero and attempt to solve: Simplifying -575 + 1350n + 18n2 = 0 Solving -575 + 1350n + 18n2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -31.94444444 + 75n + n2 = 0 Move the constant term to the right: Add '31.94444444' to each side of the equation. -31.94444444 + 75n + 31.94444444 + n2 = 0 + 31.94444444 Reorder the terms: -31.94444444 + 31.94444444 + 75n + n2 = 0 + 31.94444444 Combine like terms: -31.94444444 + 31.94444444 = 0.00000000 0.00000000 + 75n + n2 = 0 + 31.94444444 75n + n2 = 0 + 31.94444444 Combine like terms: 0 + 31.94444444 = 31.94444444 75n + n2 = 31.94444444 The n term is 75n. Take half its coefficient (37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. 75n + 1406.25 + n2 = 31.94444444 + 1406.25 Reorder the terms: 1406.25 + 75n + n2 = 31.94444444 + 1406.25 Combine like terms: 31.94444444 + 1406.25 = 1438.19444444 1406.25 + 75n + n2 = 1438.19444444 Factor a perfect square on the left side: (n + 37.5)(n + 37.5) = 1438.19444444 Calculate the square root of the right side: 37.923534177 Break this problem into two subproblems by setting (n + 37.5) equal to 37.923534177 and -37.923534177.

Subproblem 1

n + 37.5 = 37.923534177 Simplifying n + 37.5 = 37.923534177 Reorder the terms: 37.5 + n = 37.923534177 Solving 37.5 + n = 37.923534177 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + n = 37.923534177 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + n = 37.923534177 + -37.5 n = 37.923534177 + -37.5 Combine like terms: 37.923534177 + -37.5 = 0.423534177 n = 0.423534177 Simplifying n = 0.423534177

Subproblem 2

n + 37.5 = -37.923534177 Simplifying n + 37.5 = -37.923534177 Reorder the terms: 37.5 + n = -37.923534177 Solving 37.5 + n = -37.923534177 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + n = -37.923534177 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + n = -37.923534177 + -37.5 n = -37.923534177 + -37.5 Combine like terms: -37.923534177 + -37.5 = -75.423534177 n = -75.423534177 Simplifying n = -75.423534177

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.423534177, -75.423534177}

Solution

n = {0.423534177, -75.423534177}

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