5c*(3c-7)-2c(5c*-8c)=

Solution for 5c*(3c-7)-2c(5c*-8c)= equation:

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

Reorder the terms:
5c(-7 + 3c) + -2c(5c * -8c) = 0
(-7 * 5c + 3c * 5c) + -2c(5c * -8c) = 0
(-35c + 15c2) + -2c(5c * -8c) = 0

Reorder the terms for easier multiplication:
-35c + 15c2 + -2c(5 * -8c * c) = 0

Multiply 5 * -8
-35c + 15c2 + -2c(-40c * c) = 0

Multiply c * c
-35c + 15c2 + -2c(-40c2) = 0

Remove parenthesis around (-40c2)
-35c + 15c2 + -2c * -40c2 = 0

Reorder the terms for easier multiplication:
-35c + 15c2 + -2 * -40c * c2 = 0

Multiply -2 * -40
-35c + 15c2 + 80c * c2 = 0

Multiply c * c2
-35c + 15c2 + 80c3 = 0

Solving
-35c + 15c2 + 80c3 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '5c'.
5c(-7 + 3c + 16c2) = 0

Ignore the factor 5.
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 '(-7 + 3c + 16c2)' equal to zero and attempt to solve:

Simplifying
-7 + 3c + 16c2 = 0

Solving
-7 + 3c + 16c2 = 0

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

Divide each side by '16'.
-0.4375 + 0.1875c + c2 = 0

Move the constant term to the right:

Add '0.4375' to each side of the equation.
-0.4375 + 0.1875c + 0.4375 + c2 = 0 + 0.4375

Reorder the terms:
-0.4375 + 0.4375 + 0.1875c + c2 = 0 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + 0.1875c + c2 = 0 + 0.4375
0.1875c + c2 = 0 + 0.4375

Combine like terms: 0 + 0.4375 = 0.4375
0.1875c + c2 = 0.4375

The c term is 0.1875c.  Take half its coefficient (0.09375).
Square it (0.0087890625) and add it to both sides.

Add '0.0087890625' to each side of the equation.
0.1875c + 0.0087890625 + c2 = 0.4375 + 0.0087890625

Reorder the terms:
0.0087890625 + 0.1875c + c2 = 0.4375 + 0.0087890625

Combine like terms: 0.4375 + 0.0087890625 = 0.4462890625
0.0087890625 + 0.1875c + c2 = 0.4462890625

Factor a perfect square on the left side:
(c + 0.09375)(c + 0.09375) = 0.4462890625

Calculate the square root of the right side: 0.668048698

Break this problem into two subproblems by setting 
(c + 0.09375) equal to 0.668048698 and -0.668048698.

Subproblem 1
c + 0.09375 = 0.668048698

Simplifying
c + 0.09375 = 0.668048698

Reorder the terms:
0.09375 + c = 0.668048698

Solving
0.09375 + c = 0.668048698

Solving for variable 'c'.

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

Add '-0.09375' to each side of the equation.
0.09375 + -0.09375 + c = 0.668048698 + -0.09375

Combine like terms: 0.09375 + -0.09375 = 0.00000
0.00000 + c = 0.668048698 + -0.09375
c = 0.668048698 + -0.09375

Combine like terms: 0.668048698 + -0.09375 = 0.574298698
c = 0.574298698

Simplifying
c = 0.574298698

Subproblem 2
c + 0.09375 = -0.668048698

Simplifying
c + 0.09375 = -0.668048698

Reorder the terms:
0.09375 + c = -0.668048698

Solving
0.09375 + c = -0.668048698

Solving for variable 'c'.

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

Add '-0.09375' to each side of the equation.
0.09375 + -0.09375 + c = -0.668048698 + -0.09375

Combine like terms: 0.09375 + -0.09375 = 0.00000
0.00000 + c = -0.668048698 + -0.09375
c = -0.668048698 + -0.09375

Combine like terms: -0.668048698 + -0.09375 = -0.761798698
c = -0.761798698

Simplifying
c = -0.761798698

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.574298698, -0.761798698}
Solution
c = {0, 0.574298698, -0.761798698}