-4(2n^2-2n)=3(n+6)

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

Simplifying
-4(2n2 + -2n) = 3(n + 6)

Reorder the terms:
-4(-2n + 2n2) = 3(n + 6)
(-2n * -4 + 2n2 * -4) = 3(n + 6)
(8n + -8n2) = 3(n + 6)

Reorder the terms:
8n + -8n2 = 3(6 + n)
8n + -8n2 = (6 * 3 + n * 3)
8n + -8n2 = (18 + 3n)

Solving
8n + -8n2 = 18 + 3n

Solving for variable 'n'.

Reorder the terms:
-18 + 8n + -3n + -8n2 = 18 + 3n + -18 + -3n

Combine like terms: 8n + -3n = 5n
-18 + 5n + -8n2 = 18 + 3n + -18 + -3n

Reorder the terms:
-18 + 5n + -8n2 = 18 + -18 + 3n + -3n

Combine like terms: 18 + -18 = 0
-18 + 5n + -8n2 = 0 + 3n + -3n
-18 + 5n + -8n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-18 + 5n + -8n2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
2.25 + -0.625n + n2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -0.625n + -2.25 + n2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -0.625n + n2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -0.625n + n2 = 0 + -2.25
-0.625n + n2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-0.625n + n2 = -2.25

The n term is -0.625n.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625n + 0.09765625 + n2 = -2.25 + 0.09765625

Reorder the terms:
0.09765625 + -0.625n + n2 = -2.25 + 0.09765625

Combine like terms: -2.25 + 0.09765625 = -2.15234375
0.09765625 + -0.625n + n2 = -2.15234375

Factor a perfect square on the left side:
(n + -0.3125)(n + -0.3125) = -2.15234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.