34-(2c+3)=2(c+3)c

Solution for 34-(2c+3)=2(c+3)c equation:

Simplifying
34 + -1(2c + 3) = 2(c + 3) * c

Reorder the terms:
34 + -1(3 + 2c) = 2(c + 3) * c
34 + (3 * -1 + 2c * -1) = 2(c + 3) * c
34 + (-3 + -2c) = 2(c + 3) * c

Combine like terms: 34 + -3 = 31
31 + -2c = 2(c + 3) * c

Reorder the terms:
31 + -2c = 2(3 + c) * c

Reorder the terms for easier multiplication:
31 + -2c = 2c(3 + c)
31 + -2c = (3 * 2c + c * 2c)
31 + -2c = (6c + 2c2)

Solving
31 + -2c = 6c + 2c2

Solving for variable 'c'.

Combine like terms: -2c + -6c = -8c
31 + -8c + -2c2 = 6c + 2c2 + -6c + -2c2

Reorder the terms:
31 + -8c + -2c2 = 6c + -6c + 2c2 + -2c2

Combine like terms: 6c + -6c = 0
31 + -8c + -2c2 = 0 + 2c2 + -2c2
31 + -8c + -2c2 = 2c2 + -2c2

Combine like terms: 2c2 + -2c2 = 0
31 + -8c + -2c2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-15.5 + 4c + c2 = 0

Move the constant term to the right:

Add '15.5' to each side of the equation.
-15.5 + 4c + 15.5 + c2 = 0 + 15.5

Reorder the terms:
-15.5 + 15.5 + 4c + c2 = 0 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + 4c + c2 = 0 + 15.5
4c + c2 = 0 + 15.5

Combine like terms: 0 + 15.5 = 15.5
4c + c2 = 15.5

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 = 15.5 + 4

Reorder the terms:
4 + 4c + c2 = 15.5 + 4

Combine like terms: 15.5 + 4 = 19.5
4 + 4c + c2 = 19.5

Factor a perfect square on the left side:
(c + 2)(c + 2) = 19.5

Calculate the square root of the right side: 4.415880433

Break this problem into two subproblems by setting 
(c + 2) equal to 4.415880433 and -4.415880433.

Subproblem 1
c + 2 = 4.415880433

Simplifying
c + 2 = 4.415880433

Reorder the terms:
2 + c = 4.415880433

Solving
2 + c = 4.415880433

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 = 4.415880433 + -2

Combine like terms: 2 + -2 = 0
0 + c = 4.415880433 + -2
c = 4.415880433 + -2

Combine like terms: 4.415880433 + -2 = 2.415880433
c = 2.415880433

Simplifying
c = 2.415880433

Subproblem 2
c + 2 = -4.415880433

Simplifying
c + 2 = -4.415880433

Reorder the terms:
2 + c = -4.415880433

Solving
2 + c = -4.415880433

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 = -4.415880433 + -2

Combine like terms: 2 + -2 = 0
0 + c = -4.415880433 + -2
c = -4.415880433 + -2

Combine like terms: -4.415880433 + -2 = -6.415880433
c = -6.415880433

Simplifying
c = -6.415880433

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {2.415880433, -6.415880433}