4n(1-9n)+4(-7n-6)=

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Solution for 4n(1-9n)+4(-7n-6)= equation: 


Simplifying
4n(1 + -9n) + 4(-7n + -6) = 0
(1 * 4n + -9n * 4n) + 4(-7n + -6) = 0
(4n + -36n2) + 4(-7n + -6) = 0

Reorder the terms:
4n + -36n2 + 4(-6 + -7n) = 0
4n + -36n2 + (-6 * 4 + -7n * 4) = 0
4n + -36n2 + (-24 + -28n) = 0

Reorder the terms:
-24 + 4n + -28n + -36n2 = 0

Combine like terms: 4n + -28n = -24n
-24 + -24n + -36n2 = 0

Solving
-24 + -24n + -36n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-12'.
-12(2 + 2n + 3n2) = 0

Ignore the factor -12.

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

Simplifying
2 + 2n + 3n2 = 0

Solving
2 + 2n + 3n2 = 0

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

Divide each side by '3'.
0.6666666667 + 0.6666666667n + n2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 0.6666666667n + -0.6666666667 + n2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 0.6666666667n + n2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 0.6666666667n + n2 = 0 + -0.6666666667
0.6666666667n + n2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
0.6666666667n + n2 = -0.6666666667

The n term is 0.6666666667n.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667n + 0.1111111112 + n2 = -0.6666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667n + n2 = -0.6666666667 + 0.1111111112

Combine like terms: -0.6666666667 + 0.1111111112 = -0.5555555555
0.1111111112 + 0.6666666667n + n2 = -0.5555555555

Factor a perfect square on the left side:
(n + 0.3333333334)(n + 0.3333333334) = -0.5555555555

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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