5(n-2)-14n=-3n(5-4n)

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Solution for 5(n-2)-14n=-3n(5-4n) equation: 


Simplifying
5(n + -2) + -14n = -3n(5 + -4n)

Reorder the terms:
5(-2 + n) + -14n = -3n(5 + -4n)
(-2 * 5 + n * 5) + -14n = -3n(5 + -4n)
(-10 + 5n) + -14n = -3n(5 + -4n)

Combine like terms: 5n + -14n = -9n
-10 + -9n = -3n(5 + -4n)
-10 + -9n = (5 * -3n + -4n * -3n)
-10 + -9n = (-15n + 12n2)

Solving
-10 + -9n = -15n + 12n2

Solving for variable 'n'.

Combine like terms: -9n + 15n = 6n
-10 + 6n + -12n2 = -15n + 12n2 + 15n + -12n2

Reorder the terms:
-10 + 6n + -12n2 = -15n + 15n + 12n2 + -12n2

Combine like terms: -15n + 15n = 0
-10 + 6n + -12n2 = 0 + 12n2 + -12n2
-10 + 6n + -12n2 = 12n2 + -12n2

Combine like terms: 12n2 + -12n2 = 0
-10 + 6n + -12n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 3n + -6n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 3n + -6n2)' equal to zero and attempt to solve:

Simplifying
-5 + 3n + -6n2 = 0

Solving
-5 + 3n + -6n2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.8333333333 + -0.5n + n2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -0.5n + -0.8333333333 + n2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -0.5n + n2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -0.5n + n2 = 0 + -0.8333333333
-0.5n + n2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-0.5n + n2 = -0.8333333333

The n term is -0.5n.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5n + 0.0625 + n2 = -0.8333333333 + 0.0625

Reorder the terms:
0.0625 + -0.5n + n2 = -0.8333333333 + 0.0625

Combine like terms: -0.8333333333 + 0.0625 = -0.7708333333
0.0625 + -0.5n + n2 = -0.7708333333

Factor a perfect square on the left side:
(n + -0.25)(n + -0.25) = -0.7708333333

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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