-6n-20=-2n*4(1-3n)

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Solution for -6n-20=-2n*4(1-3n) equation: 


Simplifying
-6n + -20 = -2n * 4(1 + -3n)

Reorder the terms:
-20 + -6n = -2n * 4(1 + -3n)

Reorder the terms for easier multiplication:
-20 + -6n = -2 * 4n(1 + -3n)

Multiply -2 * 4
-20 + -6n = -8n(1 + -3n)
-20 + -6n = (1 * -8n + -3n * -8n)
-20 + -6n = (-8n + 24n2)

Solving
-20 + -6n = -8n + 24n2

Solving for variable 'n'.

Combine like terms: -6n + 8n = 2n
-20 + 2n + -24n2 = -8n + 24n2 + 8n + -24n2

Reorder the terms:
-20 + 2n + -24n2 = -8n + 8n + 24n2 + -24n2

Combine like terms: -8n + 8n = 0
-20 + 2n + -24n2 = 0 + 24n2 + -24n2
-20 + 2n + -24n2 = 24n2 + -24n2

Combine like terms: 24n2 + -24n2 = 0
-20 + 2n + -24n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + n + -12n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + n + -12n2)' equal to zero and attempt to solve:

Simplifying
-10 + n + -12n2 = 0

Solving
-10 + n + -12n2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
0.8333333333 + -0.08333333333n + n2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -0.08333333333n + -0.8333333333 + n2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -0.08333333333n + n2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -0.08333333333n + n2 = 0 + -0.8333333333
-0.08333333333n + n2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-0.08333333333n + n2 = -0.8333333333

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.08333333333n + 0.25 + n2 = -0.8333333333 + 0.25

Reorder the terms:
0.25 + -0.08333333333n + n2 = -0.8333333333 + 0.25

Combine like terms: -0.8333333333 + 0.25 = -0.5833333333
0.25 + -0.08333333333n + n2 = -0.5833333333

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = -0.5833333333

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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