10n^2-64n+70=0

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Solution for 10n^2-64n+70=0 equation:


Simplifying
10n2 + -64n + 70 = 0

Reorder the terms:
70 + -64n + 10n2 = 0

Solving
70 + -64n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + -32n + 5n2) = 0

Factor a trinomial.
2((7 + -5n)(5 + -1n)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(7 + -5n)' equal to zero and attempt to solve: Simplifying 7 + -5n = 0 Solving 7 + -5n = 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 + -5n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5n = 0 + -7 -5n = 0 + -7 Combine like terms: 0 + -7 = -7 -5n = -7 Divide each side by '-5'. n = 1.4 Simplifying n = 1.4

Subproblem 2

Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5

Solution

n = {1.4, 5}

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