(6n+1)(3n-2)-(4n-5)(3n+1)=

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Solution for (6n+1)(3n-2)-(4n-5)(3n+1)= equation: 


Simplifying
(6n + 1)(3n + -2) + -1(4n + -5)(3n + 1) = 0

Reorder the terms:
(1 + 6n)(3n + -2) + -1(4n + -5)(3n + 1) = 0

Reorder the terms:
(1 + 6n)(-2 + 3n) + -1(4n + -5)(3n + 1) = 0

Multiply (1 + 6n) * (-2 + 3n)
(1(-2 + 3n) + 6n * (-2 + 3n)) + -1(4n + -5)(3n + 1) = 0
((-2 * 1 + 3n * 1) + 6n * (-2 + 3n)) + -1(4n + -5)(3n + 1) = 0
((-2 + 3n) + 6n * (-2 + 3n)) + -1(4n + -5)(3n + 1) = 0
(-2 + 3n + (-2 * 6n + 3n * 6n)) + -1(4n + -5)(3n + 1) = 0
(-2 + 3n + (-12n + 18n2)) + -1(4n + -5)(3n + 1) = 0

Combine like terms: 3n + -12n = -9n
(-2 + -9n + 18n2) + -1(4n + -5)(3n + 1) = 0

Reorder the terms:
-2 + -9n + 18n2 + -1(-5 + 4n)(3n + 1) = 0

Reorder the terms:
-2 + -9n + 18n2 + -1(-5 + 4n)(1 + 3n) = 0

Multiply (-5 + 4n) * (1 + 3n)
-2 + -9n + 18n2 + -1(-5(1 + 3n) + 4n * (1 + 3n)) = 0
-2 + -9n + 18n2 + -1((1 * -5 + 3n * -5) + 4n * (1 + 3n)) = 0
-2 + -9n + 18n2 + -1((-5 + -15n) + 4n * (1 + 3n)) = 0
-2 + -9n + 18n2 + -1(-5 + -15n + (1 * 4n + 3n * 4n)) = 0
-2 + -9n + 18n2 + -1(-5 + -15n + (4n + 12n2)) = 0

Combine like terms: -15n + 4n = -11n
-2 + -9n + 18n2 + -1(-5 + -11n + 12n2) = 0
-2 + -9n + 18n2 + (-5 * -1 + -11n * -1 + 12n2 * -1) = 0
-2 + -9n + 18n2 + (5 + 11n + -12n2) = 0

Reorder the terms:
-2 + 5 + -9n + 11n + 18n2 + -12n2 = 0

Combine like terms: -2 + 5 = 3
3 + -9n + 11n + 18n2 + -12n2 = 0

Combine like terms: -9n + 11n = 2n
3 + 2n + 18n2 + -12n2 = 0

Combine like terms: 18n2 + -12n2 = 6n2
3 + 2n + 6n2 = 0

Solving
3 + 2n + 6n2 = 0

Solving for variable 'n'.

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

Divide each side by '6'.
0.5 + 0.3333333333n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.3333333333n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.3333333333n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.3333333333n + n2 = 0 + -0.5
0.3333333333n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.3333333333n + n2 = -0.5

The n term is 0.3333333333n.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333n + 0.02777777779 + n2 = -0.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333n + n2 = -0.5 + 0.02777777779

Combine like terms: -0.5 + 0.02777777779 = -0.47222222221
0.02777777779 + 0.3333333333n + n2 = -0.47222222221

Factor a perfect square on the left side:
(n + 0.1666666667)(n + 0.1666666667) = -0.47222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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