5c(2c^2-3c+4)+2c(7c-8)=0

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Solution for 5c(2c^2-3c+4)+2c(7c-8)=0 equation: 


Simplifying
5c(2c2 + -3c + 4) + 2c(7c + -8) = 0

Reorder the terms:
5c(4 + -3c + 2c2) + 2c(7c + -8) = 0
(4 * 5c + -3c * 5c + 2c2 * 5c) + 2c(7c + -8) = 0
(20c + -15c2 + 10c3) + 2c(7c + -8) = 0

Reorder the terms:
20c + -15c2 + 10c3 + 2c(-8 + 7c) = 0
20c + -15c2 + 10c3 + (-8 * 2c + 7c * 2c) = 0
20c + -15c2 + 10c3 + (-16c + 14c2) = 0

Reorder the terms:
20c + -16c + -15c2 + 14c2 + 10c3 = 0

Combine like terms: 20c + -16c = 4c
4c + -15c2 + 14c2 + 10c3 = 0

Combine like terms: -15c2 + 14c2 = -1c2
4c + -1c2 + 10c3 = 0

Solving
4c + -1c2 + 10c3 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), 'c'.
c(4 + -1c + 10c2) = 0


Subproblem 1
Set the factor 'c' equal to zero and attempt to solve:

Simplifying
c = 0

Solving
c = 0

Move all terms containing c to the left, all other terms to the right.

Simplifying
c = 0

Subproblem 2
Set the factor '(4 + -1c + 10c2)' equal to zero and attempt to solve:

Simplifying
4 + -1c + 10c2 = 0

Solving
4 + -1c + 10c2 = 0

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

Divide each side by '10'.
0.4 + -0.1c + c2 = 0.0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -0.1c + -0.4 + c2 = 0.0 + -0.4

Reorder the terms:
0.4 + -0.4 + -0.1c + c2 = 0.0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -0.1c + c2 = 0.0 + -0.4
-0.1c + c2 = 0.0 + -0.4

Combine like terms: 0.0 + -0.4 = -0.4
-0.1c + c2 = -0.4

The c term is -0.1c.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1c + 0.0025 + c2 = -0.4 + 0.0025

Reorder the terms:
0.0025 + -0.1c + c2 = -0.4 + 0.0025

Combine like terms: -0.4 + 0.0025 = -0.3975
0.0025 + -0.1c + c2 = -0.3975

Factor a perfect square on the left side:
(c + -0.05)(c + -0.05) = -0.3975

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.
Solution
c = {0}

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