7n=5n(10n+7)

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Solution for 7n=5n(10n+7) equation:


Simplifying
7n = 5n(10n + 7)

Reorder the terms:
7n = 5n(7 + 10n)
7n = (7 * 5n + 10n * 5n)
7n = (35n + 50n2)

Solving
7n = 35n + 50n2

Solving for variable 'n'.

Combine like terms: 7n + -35n = -28n
-28n + -50n2 = 35n + 50n2 + -35n + -50n2

Reorder the terms:
-28n + -50n2 = 35n + -35n + 50n2 + -50n2

Combine like terms: 35n + -35n = 0
-28n + -50n2 = 0 + 50n2 + -50n2
-28n + -50n2 = 50n2 + -50n2

Combine like terms: 50n2 + -50n2 = 0
-28n + -50n2 = 0

Factor out the Greatest Common Factor (GCF), '-2n'.
-2n(14 + 25n) = 0

Ignore the factor -2.

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0

Subproblem 2

Set the factor '(14 + 25n)' equal to zero and attempt to solve: Simplifying 14 + 25n = 0 Solving 14 + 25n = 0 Move all terms containing n to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 25n = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 25n = 0 + -14 25n = 0 + -14 Combine like terms: 0 + -14 = -14 25n = -14 Divide each side by '25'. n = -0.56 Simplifying n = -0.56

Solution

n = {0, -0.56}

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