3n(35-4n)=89n+45

Solution for 3n(35-4n)=89n+45 equation:

Simplifying
3n(35 + -4n) = 89n + 45
(35 * 3n + -4n * 3n) = 89n + 45
(105n + -12n2) = 89n + 45

Reorder the terms:
105n + -12n2 = 45 + 89n

Solving
105n + -12n2 = 45 + 89n

Solving for variable 'n'.

Reorder the terms:
-45 + 105n + -89n + -12n2 = 45 + 89n + -45 + -89n

Combine like terms: 105n + -89n = 16n
-45 + 16n + -12n2 = 45 + 89n + -45 + -89n

Reorder the terms:
-45 + 16n + -12n2 = 45 + -45 + 89n + -89n

Combine like terms: 45 + -45 = 0
-45 + 16n + -12n2 = 0 + 89n + -89n
-45 + 16n + -12n2 = 89n + -89n

Combine like terms: 89n + -89n = 0
-45 + 16n + -12n2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
3.75 + -1.333333333n + n2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -1.333333333n + -3.75 + n2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -1.333333333n + n2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -1.333333333n + n2 = 0 + -3.75
-1.333333333n + n2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-1.333333333n + n2 = -3.75

The n term is -1.333333333n.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333n + 0.4444444442 + n2 = -3.75 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333n + n2 = -3.75 + 0.4444444442

Combine like terms: -3.75 + 0.4444444442 = -3.3055555558
0.4444444442 + -1.333333333n + n2 = -3.3055555558

Factor a perfect square on the left side:
(n + -0.6666666665)(n + -0.6666666665) = -3.3055555558

Can't calculate square root of the right side.

The solution to this equation could not be determined.