24n^2+20n+8=0

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Solution for 24n^2+20n+8=0 equation: 


Simplifying
24n2 + 20n + 8 = 0

Reorder the terms:
8 + 20n + 24n2 = 0

Solving
8 + 20n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 5n + 6n2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + 5n + 6n2)' equal to zero and attempt to solve:

Simplifying
2 + 5n + 6n2 = 0

Solving
2 + 5n + 6n2 = 0

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

Divide each side by '6'.
0.3333333333 + 0.8333333333n + n2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 0.8333333333n + -0.3333333333 + n2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 0.8333333333n + n2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 0.8333333333n + n2 = 0 + -0.3333333333
0.8333333333n + n2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
0.8333333333n + n2 = -0.3333333333

The n term is 0.8333333333n.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333n + 0.1736111111 + n2 = -0.3333333333 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333n + n2 = -0.3333333333 + 0.1736111111

Combine like terms: -0.3333333333 + 0.1736111111 = -0.1597222222
0.1736111111 + 0.8333333333n + n2 = -0.1597222222

Factor a perfect square on the left side:
(n + 0.4166666667)(n + 0.4166666667) = -0.1597222222

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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