15n^2+35=50n

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Solution for 15n^2+35=50n equation:


Simplifying
15n2 + 35 = 50n

Reorder the terms:
35 + 15n2 = 50n

Solving
35 + 15n2 = 50n

Solving for variable 'n'.

Reorder the terms:
35 + -50n + 15n2 = 50n + -50n

Combine like terms: 50n + -50n = 0
35 + -50n + 15n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(7 + -10n + 3n2) = 0

Factor a trinomial.
5((1 + -1n)(7 + -3n)) = 0

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(7 + -3n)' equal to zero and attempt to solve: Simplifying 7 + -3n = 0 Solving 7 + -3n = 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 + -3n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3n = 0 + -7 -3n = 0 + -7 Combine like terms: 0 + -7 = -7 -3n = -7 Divide each side by '-3'. n = 2.333333333 Simplifying n = 2.333333333

Solution

n = {1, 2.333333333}

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