9n+56=7n-2n(n-2)

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Solution for 9n+56=7n-2n(n-2) equation: 


Simplifying
9n + 56 = 7n + -2n(n + -2)

Reorder the terms:
56 + 9n = 7n + -2n(n + -2)

Reorder the terms:
56 + 9n = 7n + -2n(-2 + n)
56 + 9n = 7n + (-2 * -2n + n * -2n)
56 + 9n = 7n + (4n + -2n2)

Combine like terms: 7n + 4n = 11n
56 + 9n = 11n + -2n2

Solving
56 + 9n = 11n + -2n2

Solving for variable 'n'.

Combine like terms: 9n + -11n = -2n
56 + -2n + 2n2 = 11n + -2n2 + -11n + 2n2

Reorder the terms:
56 + -2n + 2n2 = 11n + -11n + -2n2 + 2n2

Combine like terms: 11n + -11n = 0
56 + -2n + 2n2 = 0 + -2n2 + 2n2
56 + -2n + 2n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
56 + -2n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -1n + n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(28 + -1n + n2)' equal to zero and attempt to solve:

Simplifying
28 + -1n + n2 = 0

Solving
28 + -1n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -1n + -28 + n2 = 0 + -28

Reorder the terms:
28 + -28 + -1n + n2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -1n + n2 = 0 + -28
-1n + n2 = 0 + -28

Combine like terms: 0 + -28 = -28
-1n + n2 = -28

The n term is -1n.  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.
-1n + 0.25 + n2 = -28 + 0.25

Reorder the terms:
0.25 + -1n + n2 = -28 + 0.25

Combine like terms: -28 + 0.25 = -27.75
0.25 + -1n + n2 = -27.75

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = -27.75

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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