4(2c^2+4c-6)+(3-8c+c^2)-(3-8c+5c^2)=

Solution for 4(2c^2+4c-6)+(3-8c+c^2)-(3-8c+5c^2)= equation:

Simplifying
4(2c2 + 4c + -6) + (3 + -8c + c2) + -1(3 + -8c + 5c2) = 0

Reorder the terms:
4(-6 + 4c + 2c2) + (3 + -8c + c2) + -1(3 + -8c + 5c2) = 0
(-6 * 4 + 4c * 4 + 2c2 * 4) + (3 + -8c + c2) + -1(3 + -8c + 5c2) = 0
(-24 + 16c + 8c2) + (3 + -8c + c2) + -1(3 + -8c + 5c2) = 0

Remove parenthesis around (3 + -8c + c2)
-24 + 16c + 8c2 + 3 + -8c + c2 + -1(3 + -8c + 5c2) = 0
-24 + 16c + 8c2 + 3 + -8c + c2 + (3 * -1 + -8c * -1 + 5c2 * -1) = 0
-24 + 16c + 8c2 + 3 + -8c + c2 + (-3 + 8c + -5c2) = 0

Reorder the terms:
-24 + 3 + -3 + 16c + -8c + 8c + 8c2 + c2 + -5c2 = 0

Combine like terms: -24 + 3 = -21
-21 + -3 + 16c + -8c + 8c + 8c2 + c2 + -5c2 = 0

Combine like terms: -21 + -3 = -24
-24 + 16c + -8c + 8c + 8c2 + c2 + -5c2 = 0

Combine like terms: 16c + -8c = 8c
-24 + 8c + 8c + 8c2 + c2 + -5c2 = 0

Combine like terms: 8c + 8c = 16c
-24 + 16c + 8c2 + c2 + -5c2 = 0

Combine like terms: 8c2 + c2 = 9c2
-24 + 16c + 9c2 + -5c2 = 0

Combine like terms: 9c2 + -5c2 = 4c2
-24 + 16c + 4c2 = 0

Solving
-24 + 16c + 4c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 4c + c2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + 4c + c2)' equal to zero and attempt to solve:

Simplifying
-6 + 4c + c2 = 0

Solving
-6 + 4c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 4c + 6 + c2 = 0 + 6

Reorder the terms:
-6 + 6 + 4c + c2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 4c + c2 = 0 + 6
4c + c2 = 0 + 6

Combine like terms: 0 + 6 = 6
4c + c2 = 6

The c term is 4c.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4c + 4 + c2 = 6 + 4

Reorder the terms:
4 + 4c + c2 = 6 + 4

Combine like terms: 6 + 4 = 10
4 + 4c + c2 = 10

Factor a perfect square on the left side:
(c + 2)(c + 2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(c + 2) equal to 3.16227766 and -3.16227766.

Subproblem 1
c + 2 = 3.16227766

Simplifying
c + 2 = 3.16227766

Reorder the terms:
2 + c = 3.16227766

Solving
2 + c = 3.16227766

Solving for variable 'c'.

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

Add '-2' to each side of the equation.
2 + -2 + c = 3.16227766 + -2

Combine like terms: 2 + -2 = 0
0 + c = 3.16227766 + -2
c = 3.16227766 + -2

Combine like terms: 3.16227766 + -2 = 1.16227766
c = 1.16227766

Simplifying
c = 1.16227766

Subproblem 2
c + 2 = -3.16227766

Simplifying
c + 2 = -3.16227766

Reorder the terms:
2 + c = -3.16227766

Solving
2 + c = -3.16227766

Solving for variable 'c'.

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

Add '-2' to each side of the equation.
2 + -2 + c = -3.16227766 + -2

Combine like terms: 2 + -2 = 0
0 + c = -3.16227766 + -2
c = -3.16227766 + -2

Combine like terms: -3.16227766 + -2 = -5.16227766
c = -5.16227766

Simplifying
c = -5.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.16227766, -5.16227766}
Solution
c = {1.16227766, -5.16227766}