-5n(4-3n)=10(n-2)

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Solution for -5n(4-3n)=10(n-2) equation: 


Simplifying
-5n(4 + -3n) = 10(n + -2)
(4 * -5n + -3n * -5n) = 10(n + -2)
(-20n + 15n2) = 10(n + -2)

Reorder the terms:
-20n + 15n2 = 10(-2 + n)
-20n + 15n2 = (-2 * 10 + n * 10)
-20n + 15n2 = (-20 + 10n)

Solving
-20n + 15n2 = -20 + 10n

Solving for variable 'n'.

Reorder the terms:
20 + -20n + -10n + 15n2 = -20 + 10n + 20 + -10n

Combine like terms: -20n + -10n = -30n
20 + -30n + 15n2 = -20 + 10n + 20 + -10n

Reorder the terms:
20 + -30n + 15n2 = -20 + 20 + 10n + -10n

Combine like terms: -20 + 20 = 0
20 + -30n + 15n2 = 0 + 10n + -10n
20 + -30n + 15n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
20 + -30n + 15n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + -6n + 3n2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(4 + -6n + 3n2)' equal to zero and attempt to solve:

Simplifying
4 + -6n + 3n2 = 0

Solving
4 + -6n + 3n2 = 0

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

Divide each side by '3'.
1.333333333 + -2n + n2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -2n + -1.333333333 + n2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -2n + n2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -2n + n2 = 0 + -1.333333333
-2n + n2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-2n + n2 = -1.333333333

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = -1.333333333 + 1

Reorder the terms:
1 + -2n + n2 = -1.333333333 + 1

Combine like terms: -1.333333333 + 1 = -0.333333333
1 + -2n + n2 = -0.333333333

Factor a perfect square on the left side:
(n + -1)(n + -1) = -0.333333333

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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