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

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


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

Reorder the terms:
4(-5 + 2n) = 2n(3n + -3)
(-5 * 4 + 2n * 4) = 2n(3n + -3)
(-20 + 8n) = 2n(3n + -3)

Reorder the terms:
-20 + 8n = 2n(-3 + 3n)
-20 + 8n = (-3 * 2n + 3n * 2n)
-20 + 8n = (-6n + 6n2)

Solving
-20 + 8n = -6n + 6n2

Solving for variable 'n'.

Combine like terms: 8n + 6n = 14n
-20 + 14n + -6n2 = -6n + 6n2 + 6n + -6n2

Reorder the terms:
-20 + 14n + -6n2 = -6n + 6n + 6n2 + -6n2

Combine like terms: -6n + 6n = 0
-20 + 14n + -6n2 = 0 + 6n2 + -6n2
-20 + 14n + -6n2 = 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
-20 + 14n + -6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 7n + -3n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + 7n + -3n2)' equal to zero and attempt to solve:

Simplifying
-10 + 7n + -3n2 = 0

Solving
-10 + 7n + -3n2 = 0

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

Divide each side by '-3'.
3.333333333 + -2.333333333n + n2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -2.333333333n + -3.333333333 + n2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -2.333333333n + n2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -2.333333333n + n2 = 0 + -3.333333333
-2.333333333n + n2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-2.333333333n + n2 = -3.333333333

The n term is -2.333333333n.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333n + 1.361111112 + n2 = -3.333333333 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333n + n2 = -3.333333333 + 1.361111112

Combine like terms: -3.333333333 + 1.361111112 = -1.972222221
1.361111112 + -2.333333333n + n2 = -1.972222221

Factor a perfect square on the left side:
(n + -1.166666667)(n + -1.166666667) = -1.972222221

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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