20-6n=-2n(n+6)

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Solution for 20-6n=-2n(n+6) equation: 


Simplifying
20 + -6n = -2n(n + 6)

Reorder the terms:
20 + -6n = -2n(6 + n)
20 + -6n = (6 * -2n + n * -2n)
20 + -6n = (-12n + -2n2)

Solving
20 + -6n = -12n + -2n2

Solving for variable 'n'.

Combine like terms: -6n + 12n = 6n
20 + 6n + 2n2 = -12n + -2n2 + 12n + 2n2

Reorder the terms:
20 + 6n + 2n2 = -12n + 12n + -2n2 + 2n2

Combine like terms: -12n + 12n = 0
20 + 6n + 2n2 = 0 + -2n2 + 2n2
20 + 6n + 2n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
20 + 6n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 3n + n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + 3n + n2)' equal to zero and attempt to solve:

Simplifying
10 + 3n + n2 = 0

Solving
10 + 3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 3n + -10 + n2 = 0 + -10

Reorder the terms:
10 + -10 + 3n + n2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3n + n2 = 0 + -10
3n + n2 = 0 + -10

Combine like terms: 0 + -10 = -10
3n + n2 = -10

The n term is 3n.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3n + 2.25 + n2 = -10 + 2.25

Reorder the terms:
2.25 + 3n + n2 = -10 + 2.25

Combine like terms: -10 + 2.25 = -7.75
2.25 + 3n + n2 = -7.75

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = -7.75

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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