4n(1+5n)+2(1-8n)=

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Solution for 4n(1+5n)+2(1-8n)= equation: 


Simplifying
4n(1 + 5n) + 2(1 + -8n) = 0
(1 * 4n + 5n * 4n) + 2(1 + -8n) = 0
(4n + 20n2) + 2(1 + -8n) = 0
4n + 20n2 + (1 * 2 + -8n * 2) = 0
4n + 20n2 + (2 + -16n) = 0

Reorder the terms:
2 + 4n + -16n + 20n2 = 0

Combine like terms: 4n + -16n = -12n
2 + -12n + 20n2 = 0

Solving
2 + -12n + 20n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6n + 10n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -6n + 10n2)' equal to zero and attempt to solve:

Simplifying
1 + -6n + 10n2 = 0

Solving
1 + -6n + 10n2 = 0

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

Divide each side by '10'.
0.1 + -0.6n + n2 = 0.0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -0.6n + -0.1 + n2 = 0.0 + -0.1

Reorder the terms:
0.1 + -0.1 + -0.6n + n2 = 0.0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -0.6n + n2 = 0.0 + -0.1
-0.6n + n2 = 0.0 + -0.1

Combine like terms: 0.0 + -0.1 = -0.1
-0.6n + n2 = -0.1

The n term is -0.6n.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6n + 0.09 + n2 = -0.1 + 0.09

Reorder the terms:
0.09 + -0.6n + n2 = -0.1 + 0.09

Combine like terms: -0.1 + 0.09 = -0.01
0.09 + -0.6n + n2 = -0.01

Factor a perfect square on the left side:
(n + -0.3)(n + -0.3) = -0.01

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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