17n^2-41n=-10-4n^2

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Solution for 17n^2-41n=-10-4n^2 equation: 


Simplifying
17n2 + -41n = -10 + -4n2

Reorder the terms:
-41n + 17n2 = -10 + -4n2

Solving
-41n + 17n2 = -10 + -4n2

Solving for variable 'n'.

Reorder the terms:
10 + -41n + 17n2 + 4n2 = -10 + -4n2 + 10 + 4n2

Combine like terms: 17n2 + 4n2 = 21n2
10 + -41n + 21n2 = -10 + -4n2 + 10 + 4n2

Reorder the terms:
10 + -41n + 21n2 = -10 + 10 + -4n2 + 4n2

Combine like terms: -10 + 10 = 0
10 + -41n + 21n2 = 0 + -4n2 + 4n2
10 + -41n + 21n2 = -4n2 + 4n2

Combine like terms: -4n2 + 4n2 = 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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