5n^2+6n+7=n^2-4n

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Solution for 5n^2+6n+7=n^2-4n equation: 


Simplifying
5n2 + 6n + 7 = n2 + -4n

Reorder the terms:
7 + 6n + 5n2 = n2 + -4n

Reorder the terms:
7 + 6n + 5n2 = -4n + n2

Solving
7 + 6n + 5n2 = -4n + n2

Solving for variable 'n'.

Reorder the terms:
7 + 6n + 4n + 5n2 + -1n2 = -4n + n2 + 4n + -1n2

Combine like terms: 6n + 4n = 10n
7 + 10n + 5n2 + -1n2 = -4n + n2 + 4n + -1n2

Combine like terms: 5n2 + -1n2 = 4n2
7 + 10n + 4n2 = -4n + n2 + 4n + -1n2

Reorder the terms:
7 + 10n + 4n2 = -4n + 4n + n2 + -1n2

Combine like terms: -4n + 4n = 0
7 + 10n + 4n2 = 0 + n2 + -1n2
7 + 10n + 4n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
7 + 10n + 4n2 = 0

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

Divide each side by '4'.
1.75 + 2.5n + n2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 2.5n + -1.75 + n2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + 2.5n + n2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 2.5n + n2 = 0 + -1.75
2.5n + n2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
2.5n + n2 = -1.75

The n term is 2.5n.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5n + 1.5625 + n2 = -1.75 + 1.5625

Reorder the terms:
1.5625 + 2.5n + n2 = -1.75 + 1.5625

Combine like terms: -1.75 + 1.5625 = -0.1875
1.5625 + 2.5n + n2 = -0.1875

Factor a perfect square on the left side:
(n + 1.25)(n + 1.25) = -0.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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