-5n^2+30n-45=10

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Solution for -5n^2+30n-45=10 equation: 


Simplifying
-5n2 + 30n + -45 = 10

Reorder the terms:
-45 + 30n + -5n2 = 10

Solving
-45 + 30n + -5n2 = 10

Solving for variable 'n'.

Reorder the terms:
-45 + -10 + 30n + -5n2 = 10 + -10

Combine like terms: -45 + -10 = -55
-55 + 30n + -5n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-55 + 30n + -5n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-11 + 6n + -1n2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-11 + 6n + -1n2)' equal to zero and attempt to solve:

Simplifying
-11 + 6n + -1n2 = 0

Solving
-11 + 6n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
11 + -6n + n2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -6n + -11 + n2 = 0 + -11

Reorder the terms:
11 + -11 + -6n + n2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -6n + n2 = 0 + -11
-6n + n2 = 0 + -11

Combine like terms: 0 + -11 = -11
-6n + n2 = -11

The n term is -6n.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6n + 9 + n2 = -11 + 9

Reorder the terms:
9 + -6n + n2 = -11 + 9

Combine like terms: -11 + 9 = -2
9 + -6n + n2 = -2

Factor a perfect square on the left side:
(n + -3)(n + -3) = -2

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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