-3n(4n+3)=6

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


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

Reorder the terms:
-3n(3 + 4n) = 6
(3 * -3n + 4n * -3n) = 6
(-9n + -12n2) = 6

Solving
-9n + -12n2 = 6

Solving for variable 'n'.

Reorder the terms:
-6 + -9n + -12n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -9n + -12n2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(2 + 3n + 4n2) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(2 + 3n + 4n2)' equal to zero and attempt to solve:

Simplifying
2 + 3n + 4n2 = 0

Solving
2 + 3n + 4n2 = 0

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

Divide each side by '4'.
0.5 + 0.75n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.75n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.75n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.75n + n2 = 0 + -0.5
0.75n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.75n + n2 = -0.5

The n term is 0.75n.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75n + 0.140625 + n2 = -0.5 + 0.140625

Reorder the terms:
0.140625 + 0.75n + n2 = -0.5 + 0.140625

Combine like terms: -0.5 + 0.140625 = -0.359375
0.140625 + 0.75n + n2 = -0.359375

Factor a perfect square on the left side:
(n + 0.375)(n + 0.375) = -0.359375

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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