2c(c+3)+(c+5)(3c-1)=

Solution for 2c(c+3)+(c+5)(3c-1)= equation:

Simplifying
2c(c + 3) + (c + 5)(3c + -1) = 0

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

Reorder the terms:
6c + 2c2 + (5 + c)(3c + -1) = 0

Reorder the terms:
6c + 2c2 + (5 + c)(-1 + 3c) = 0

Multiply (5 + c) * (-1 + 3c)
6c + 2c2 + (5(-1 + 3c) + c(-1 + 3c)) = 0
6c + 2c2 + ((-1 * 5 + 3c * 5) + c(-1 + 3c)) = 0
6c + 2c2 + ((-5 + 15c) + c(-1 + 3c)) = 0
6c + 2c2 + (-5 + 15c + (-1 * c + 3c * c)) = 0
6c + 2c2 + (-5 + 15c + (-1c + 3c2)) = 0

Combine like terms: 15c + -1c = 14c
6c + 2c2 + (-5 + 14c + 3c2) = 0

Reorder the terms:
-5 + 6c + 14c + 2c2 + 3c2 = 0

Combine like terms: 6c + 14c = 20c
-5 + 20c + 2c2 + 3c2 = 0

Combine like terms: 2c2 + 3c2 = 5c2
-5 + 20c + 5c2 = 0

Solving
-5 + 20c + 5c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 4c + c2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + 4c + c2)' equal to zero and attempt to solve:

Simplifying
-1 + 4c + c2 = 0

Solving
-1 + 4c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4c + 1 + c2 = 0 + 1

Reorder the terms:
-1 + 1 + 4c + c2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4c + c2 = 0 + 1
4c + c2 = 0 + 1

Combine like terms: 0 + 1 = 1
4c + c2 = 1

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 = 1 + 4

Reorder the terms:
4 + 4c + c2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + 4c + c2 = 5

Factor a perfect square on the left side:
(c + 2)(c + 2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(c + 2) equal to 2.236067978 and -2.236067978.

Subproblem 1
c + 2 = 2.236067978

Simplifying
c + 2 = 2.236067978

Reorder the terms:
2 + c = 2.236067978

Solving
2 + c = 2.236067978

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 = 2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + c = 2.236067978 + -2
c = 2.236067978 + -2

Combine like terms: 2.236067978 + -2 = 0.236067978
c = 0.236067978

Simplifying
c = 0.236067978

Subproblem 2
c + 2 = -2.236067978

Simplifying
c + 2 = -2.236067978

Reorder the terms:
2 + c = -2.236067978

Solving
2 + c = -2.236067978

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 = -2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + c = -2.236067978 + -2
c = -2.236067978 + -2

Combine like terms: -2.236067978 + -2 = -4.236067978
c = -4.236067978

Simplifying
c = -4.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.236067978, -4.236067978}
Solution
c = {0.236067978, -4.236067978}