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

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


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

Reorder the terms:
3(-6 + n) = 2(-2 + 6n) * 5n
(-6 * 3 + n * 3) = 2(-2 + 6n) * 5n
(-18 + 3n) = 2(-2 + 6n) * 5n

Reorder the terms for easier multiplication:
-18 + 3n = 2 * 5n(-2 + 6n)

Multiply 2 * 5
-18 + 3n = 10n(-2 + 6n)
-18 + 3n = (-2 * 10n + 6n * 10n)
-18 + 3n = (-20n + 60n2)

Solving
-18 + 3n = -20n + 60n2

Solving for variable 'n'.

Combine like terms: 3n + 20n = 23n
-18 + 23n + -60n2 = -20n + 60n2 + 20n + -60n2

Reorder the terms:
-18 + 23n + -60n2 = -20n + 20n + 60n2 + -60n2

Combine like terms: -20n + 20n = 0
-18 + 23n + -60n2 = 0 + 60n2 + -60n2
-18 + 23n + -60n2 = 60n2 + -60n2

Combine like terms: 60n2 + -60n2 = 0
-18 + 23n + -60n2 = 0

Begin completing the square.  Divide all terms by
-60 the coefficient of the squared term: 

Divide each side by '-60'.
0.3 + -0.3833333333n + n2 = 0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + -0.3833333333n + -0.3 + n2 = 0 + -0.3

Reorder the terms:
0.3 + -0.3 + -0.3833333333n + n2 = 0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + -0.3833333333n + n2 = 0 + -0.3
-0.3833333333n + n2 = 0 + -0.3

Combine like terms: 0 + -0.3 = -0.3
-0.3833333333n + n2 = -0.3

The n term is -0.3833333333n.  Take half its coefficient (-0.1916666667).
Square it (0.03673611112) and add it to both sides.

Add '0.03673611112' to each side of the equation.
-0.3833333333n + 0.03673611112 + n2 = -0.3 + 0.03673611112

Reorder the terms:
0.03673611112 + -0.3833333333n + n2 = -0.3 + 0.03673611112

Combine like terms: -0.3 + 0.03673611112 = -0.26326388888
0.03673611112 + -0.3833333333n + n2 = -0.26326388888

Factor a perfect square on the left side:
(n + -0.1916666667)(n + -0.1916666667) = -0.26326388888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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