8(2n-5)=3n(6n-2)

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Solution for 8(2n-5)=3n(6n-2) equation: 


Simplifying
8(2n + -5) = 3n(6n + -2)

Reorder the terms:
8(-5 + 2n) = 3n(6n + -2)
(-5 * 8 + 2n * 8) = 3n(6n + -2)
(-40 + 16n) = 3n(6n + -2)

Reorder the terms:
-40 + 16n = 3n(-2 + 6n)
-40 + 16n = (-2 * 3n + 6n * 3n)
-40 + 16n = (-6n + 18n2)

Solving
-40 + 16n = -6n + 18n2

Solving for variable 'n'.

Combine like terms: 16n + 6n = 22n
-40 + 22n + -18n2 = -6n + 18n2 + 6n + -18n2

Reorder the terms:
-40 + 22n + -18n2 = -6n + 6n + 18n2 + -18n2

Combine like terms: -6n + 6n = 0
-40 + 22n + -18n2 = 0 + 18n2 + -18n2
-40 + 22n + -18n2 = 18n2 + -18n2

Combine like terms: 18n2 + -18n2 = 0
-40 + 22n + -18n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 11n + -9n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + 11n + -9n2)' equal to zero and attempt to solve:

Simplifying
-20 + 11n + -9n2 = 0

Solving
-20 + 11n + -9n2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
2.222222222 + -1.222222222n + n2 = 0

Move the constant term to the right:

Add '-2.222222222' to each side of the equation.
2.222222222 + -1.222222222n + -2.222222222 + n2 = 0 + -2.222222222

Reorder the terms:
2.222222222 + -2.222222222 + -1.222222222n + n2 = 0 + -2.222222222

Combine like terms: 2.222222222 + -2.222222222 = 0.000000000
0.000000000 + -1.222222222n + n2 = 0 + -2.222222222
-1.222222222n + n2 = 0 + -2.222222222

Combine like terms: 0 + -2.222222222 = -2.222222222
-1.222222222n + n2 = -2.222222222

The n term is -1.222222222n.  Take half its coefficient (-0.611111111).
Square it (0.3734567900) and add it to both sides.

Add '0.3734567900' to each side of the equation.
-1.222222222n + 0.3734567900 + n2 = -2.222222222 + 0.3734567900

Reorder the terms:
0.3734567900 + -1.222222222n + n2 = -2.222222222 + 0.3734567900

Combine like terms: -2.222222222 + 0.3734567900 = -1.848765432
0.3734567900 + -1.222222222n + n2 = -1.848765432

Factor a perfect square on the left side:
(n + -0.611111111)(n + -0.611111111) = -1.848765432

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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