3n^2=105n-1026

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Solution for 3n^2=105n-1026 equation: 


Simplifying
3n2 = 105n + -1026

Reorder the terms:
3n2 = -1026 + 105n

Solving
3n2 = -1026 + 105n

Solving for variable 'n'.

Reorder the terms:
1026 + -105n + 3n2 = -1026 + 105n + 1026 + -105n

Reorder the terms:
1026 + -105n + 3n2 = -1026 + 1026 + 105n + -105n

Combine like terms: -1026 + 1026 = 0
1026 + -105n + 3n2 = 0 + 105n + -105n
1026 + -105n + 3n2 = 105n + -105n

Combine like terms: 105n + -105n = 0
1026 + -105n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(342 + -35n + n2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(342 + -35n + n2)' equal to zero and attempt to solve:

Simplifying
342 + -35n + n2 = 0

Solving
342 + -35n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-342' to each side of the equation.
342 + -35n + -342 + n2 = 0 + -342

Reorder the terms:
342 + -342 + -35n + n2 = 0 + -342

Combine like terms: 342 + -342 = 0
0 + -35n + n2 = 0 + -342
-35n + n2 = 0 + -342

Combine like terms: 0 + -342 = -342
-35n + n2 = -342

The n term is -35n.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35n + 306.25 + n2 = -342 + 306.25

Reorder the terms:
306.25 + -35n + n2 = -342 + 306.25

Combine like terms: -342 + 306.25 = -35.75
306.25 + -35n + n2 = -35.75

Factor a perfect square on the left side:
(n + -17.5)(n + -17.5) = -35.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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