43-(2c+4)=2(c+7)c

Solution for 43-(2c+4)=2(c+7)c equation:

Simplifying
43 + -1(2c + 4) = 2(c + 7) * c

Reorder the terms:
43 + -1(4 + 2c) = 2(c + 7) * c
43 + (4 * -1 + 2c * -1) = 2(c + 7) * c
43 + (-4 + -2c) = 2(c + 7) * c

Combine like terms: 43 + -4 = 39
39 + -2c = 2(c + 7) * c

Reorder the terms:
39 + -2c = 2(7 + c) * c

Reorder the terms for easier multiplication:
39 + -2c = 2c(7 + c)
39 + -2c = (7 * 2c + c * 2c)
39 + -2c = (14c + 2c2)

Solving
39 + -2c = 14c + 2c2

Solving for variable 'c'.

Combine like terms: -2c + -14c = -16c
39 + -16c + -2c2 = 14c + 2c2 + -14c + -2c2

Reorder the terms:
39 + -16c + -2c2 = 14c + -14c + 2c2 + -2c2

Combine like terms: 14c + -14c = 0
39 + -16c + -2c2 = 0 + 2c2 + -2c2
39 + -16c + -2c2 = 2c2 + -2c2

Combine like terms: 2c2 + -2c2 = 0
39 + -16c + -2c2 = 0

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

Divide each side by '-2'.
-19.5 + 8c + c2 = 0

Move the constant term to the right:

Add '19.5' to each side of the equation.
-19.5 + 8c + 19.5 + c2 = 0 + 19.5

Reorder the terms:
-19.5 + 19.5 + 8c + c2 = 0 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + 8c + c2 = 0 + 19.5
8c + c2 = 0 + 19.5

Combine like terms: 0 + 19.5 = 19.5
8c + c2 = 19.5

The c term is 8c.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8c + 16 + c2 = 19.5 + 16

Reorder the terms:
16 + 8c + c2 = 19.5 + 16

Combine like terms: 19.5 + 16 = 35.5
16 + 8c + c2 = 35.5

Factor a perfect square on the left side:
(c + 4)(c + 4) = 35.5

Calculate the square root of the right side: 5.958187644

Break this problem into two subproblems by setting 
(c + 4) equal to 5.958187644 and -5.958187644.

Subproblem 1
c + 4 = 5.958187644

Simplifying
c + 4 = 5.958187644

Reorder the terms:
4 + c = 5.958187644

Solving
4 + c = 5.958187644

Solving for variable 'c'.

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

Add '-4' to each side of the equation.
4 + -4 + c = 5.958187644 + -4

Combine like terms: 4 + -4 = 0
0 + c = 5.958187644 + -4
c = 5.958187644 + -4

Combine like terms: 5.958187644 + -4 = 1.958187644
c = 1.958187644

Simplifying
c = 1.958187644

Subproblem 2
c + 4 = -5.958187644

Simplifying
c + 4 = -5.958187644

Reorder the terms:
4 + c = -5.958187644

Solving
4 + c = -5.958187644

Solving for variable 'c'.

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

Add '-4' to each side of the equation.
4 + -4 + c = -5.958187644 + -4

Combine like terms: 4 + -4 = 0
0 + c = -5.958187644 + -4
c = -5.958187644 + -4

Combine like terms: -5.958187644 + -4 = -9.958187644
c = -9.958187644

Simplifying
c = -9.958187644

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.958187644, -9.958187644}