(4n+2)+(2n-3)(3n-2)=

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

Simplifying
(4n + 2) + (2n + -3)(3n + -2) = 0

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

Remove parenthesis around (2 + 4n)
2 + 4n + (2n + -3)(3n + -2) = 0

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

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

Multiply (-3 + 2n) * (-2 + 3n)
2 + 4n + (-3(-2 + 3n) + 2n * (-2 + 3n)) = 0
2 + 4n + ((-2 * -3 + 3n * -3) + 2n * (-2 + 3n)) = 0
2 + 4n + ((6 + -9n) + 2n * (-2 + 3n)) = 0
2 + 4n + (6 + -9n + (-2 * 2n + 3n * 2n)) = 0
2 + 4n + (6 + -9n + (-4n + 6n2)) = 0

Combine like terms: -9n + -4n = -13n
2 + 4n + (6 + -13n + 6n2) = 0

Reorder the terms:
2 + 6 + 4n + -13n + 6n2 = 0

Combine like terms: 2 + 6 = 8
8 + 4n + -13n + 6n2 = 0

Combine like terms: 4n + -13n = -9n
8 + -9n + 6n2 = 0

Solving
8 + -9n + 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'.
1.333333333 + -1.5n + n2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -1.5n + -1.333333333 + n2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -1.5n + n2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -1.5n + n2 = 0 + -1.333333333
-1.5n + n2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-1.5n + n2 = -1.333333333

The n term is -1.5n.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5n + 0.5625 + n2 = -1.333333333 + 0.5625

Reorder the terms:
0.5625 + -1.5n + n2 = -1.333333333 + 0.5625

Combine like terms: -1.333333333 + 0.5625 = -0.770833333
0.5625 + -1.5n + n2 = -0.770833333

Factor a perfect square on the left side:
(n + -0.75)(n + -0.75) = -0.770833333

Can't calculate square root of the right side.

The solution to this equation could not be determined.