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

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

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

Reorder the terms:
3(-4 + c) + 5(c2 + 4c + -8) = 0
(-4 * 3 + c * 3) + 5(c2 + 4c + -8) = 0
(-12 + 3c) + 5(c2 + 4c + -8) = 0

Reorder the terms:
-12 + 3c + 5(-8 + 4c + c2) = 0
-12 + 3c + (-8 * 5 + 4c * 5 + c2 * 5) = 0
-12 + 3c + (-40 + 20c + 5c2) = 0

Reorder the terms:
-12 + -40 + 3c + 20c + 5c2 = 0

Combine like terms: -12 + -40 = -52
-52 + 3c + 20c + 5c2 = 0

Combine like terms: 3c + 20c = 23c
-52 + 23c + 5c2 = 0

Solving
-52 + 23c + 5c2 = 0

Solving for variable 'c'.

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

Divide each side by '5'.
-10.4 + 4.6c + c2 = 0

Move the constant term to the right:

Add '10.4' to each side of the equation.
-10.4 + 4.6c + 10.4 + c2 = 0 + 10.4

Reorder the terms:
-10.4 + 10.4 + 4.6c + c2 = 0 + 10.4

Combine like terms: -10.4 + 10.4 = 0.0
0.0 + 4.6c + c2 = 0 + 10.4
4.6c + c2 = 0 + 10.4

Combine like terms: 0 + 10.4 = 10.4
4.6c + c2 = 10.4

The c term is 4.6c.  Take half its coefficient (2.3).
Square it (5.29) and add it to both sides.

Add '5.29' to each side of the equation.
4.6c + 5.29 + c2 = 10.4 + 5.29

Reorder the terms:
5.29 + 4.6c + c2 = 10.4 + 5.29

Combine like terms: 10.4 + 5.29 = 15.69
5.29 + 4.6c + c2 = 15.69

Factor a perfect square on the left side:
(c + 2.3)(c + 2.3) = 15.69

Calculate the square root of the right side: 3.961060464

Break this problem into two subproblems by setting 
(c + 2.3) equal to 3.961060464 and -3.961060464.

Subproblem 1
c + 2.3 = 3.961060464

Simplifying
c + 2.3 = 3.961060464

Reorder the terms:
2.3 + c = 3.961060464

Solving
2.3 + c = 3.961060464

Solving for variable 'c'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + c = 3.961060464 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + c = 3.961060464 + -2.3
c = 3.961060464 + -2.3

Combine like terms: 3.961060464 + -2.3 = 1.661060464
c = 1.661060464

Simplifying
c = 1.661060464

Subproblem 2
c + 2.3 = -3.961060464

Simplifying
c + 2.3 = -3.961060464

Reorder the terms:
2.3 + c = -3.961060464

Solving
2.3 + c = -3.961060464

Solving for variable 'c'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + c = -3.961060464 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + c = -3.961060464 + -2.3
c = -3.961060464 + -2.3

Combine like terms: -3.961060464 + -2.3 = -6.261060464
c = -6.261060464

Simplifying
c = -6.261060464

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.661060464, -6.261060464}