21n^2-41n=-10

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Solution for 21n^2-41n=-10 equation:


Simplifying
21n2 + -41n = -10

Reorder the terms:
-41n + 21n2 = -10

Solving
-41n + 21n2 = -10

Solving for variable 'n'.

Reorder the terms:
10 + -41n + 21n2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -41n + 21n2 = 0

Factor a trinomial.
(2 + -7n)(5 + -3n) = 0

Subproblem 1

Set the factor '(2 + -7n)' equal to zero and attempt to solve: Simplifying 2 + -7n = 0 Solving 2 + -7n = 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 + -7n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7n = 0 + -2 -7n = 0 + -2 Combine like terms: 0 + -2 = -2 -7n = -2 Divide each side by '-7'. n = 0.2857142857 Simplifying n = 0.2857142857

Subproblem 2

Set the factor '(5 + -3n)' equal to zero and attempt to solve: Simplifying 5 + -3n = 0 Solving 5 + -3n = 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 + -3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n = 0 + -5 -3n = 0 + -5 Combine like terms: 0 + -5 = -5 -3n = -5 Divide each side by '-3'. n = 1.666666667 Simplifying n = 1.666666667

Solution

n = {0.2857142857, 1.666666667}

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