(4c^2+8c-9)+(14c^2-6c+15)+(c-8)=

Solution for (4c^2+8c-9)+(14c^2-6c+15)+(c-8)= equation:

Simplifying
(4c2 + 8c + -9) + (14c2 + -6c + 15) + (c + -8) = 0

Reorder the terms:
(-9 + 8c + 4c2) + (14c2 + -6c + 15) + (c + -8) = 0

Remove parenthesis around (-9 + 8c + 4c2)
-9 + 8c + 4c2 + (14c2 + -6c + 15) + (c + -8) = 0

Reorder the terms:
-9 + 8c + 4c2 + (15 + -6c + 14c2) + (c + -8) = 0

Remove parenthesis around (15 + -6c + 14c2)
-9 + 8c + 4c2 + 15 + -6c + 14c2 + (c + -8) = 0

Reorder the terms:
-9 + 8c + 4c2 + 15 + -6c + 14c2 + (-8 + c) = 0

Remove parenthesis around (-8 + c)
-9 + 8c + 4c2 + 15 + -6c + 14c2 + -8 + c = 0

Reorder the terms:
-9 + 15 + -8 + 8c + -6c + c + 4c2 + 14c2 = 0

Combine like terms: -9 + 15 = 6
6 + -8 + 8c + -6c + c + 4c2 + 14c2 = 0

Combine like terms: 6 + -8 = -2
-2 + 8c + -6c + c + 4c2 + 14c2 = 0

Combine like terms: 8c + -6c = 2c
-2 + 2c + c + 4c2 + 14c2 = 0

Combine like terms: 2c + c = 3c
-2 + 3c + 4c2 + 14c2 = 0

Combine like terms: 4c2 + 14c2 = 18c2
-2 + 3c + 18c2 = 0

Solving
-2 + 3c + 18c2 = 0

Solving for variable 'c'.

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

Divide each side by '18'.
-0.1111111111 + 0.1666666667c + c2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.1666666667c + 0.1111111111 + c2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + 0.1666666667c + c2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + 0.1666666667c + c2 = 0 + 0.1111111111
0.1666666667c + c2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
0.1666666667c + c2 = 0.1111111111

The c term is 0.1666666667c.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667c + 0.006944444447 + c2 = 0.1111111111 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667c + c2 = 0.1111111111 + 0.006944444447

Combine like terms: 0.1111111111 + 0.006944444447 = 0.118055555547
0.006944444447 + 0.1666666667c + c2 = 0.118055555547

Factor a perfect square on the left side:
(c + 0.08333333335)(c + 0.08333333335) = 0.118055555547

Calculate the square root of the right side: 0.343592135

Break this problem into two subproblems by setting 
(c + 0.08333333335) equal to 0.343592135 and -0.343592135.

Subproblem 1
c + 0.08333333335 = 0.343592135

Simplifying
c + 0.08333333335 = 0.343592135

Reorder the terms:
0.08333333335 + c = 0.343592135

Solving
0.08333333335 + c = 0.343592135

Solving for variable 'c'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + c = 0.343592135 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + c = 0.343592135 + -0.08333333335
c = 0.343592135 + -0.08333333335

Combine like terms: 0.343592135 + -0.08333333335 = 0.26025880165
c = 0.26025880165

Simplifying
c = 0.26025880165

Subproblem 2
c + 0.08333333335 = -0.343592135

Simplifying
c + 0.08333333335 = -0.343592135

Reorder the terms:
0.08333333335 + c = -0.343592135

Solving
0.08333333335 + c = -0.343592135

Solving for variable 'c'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + c = -0.343592135 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + c = -0.343592135 + -0.08333333335
c = -0.343592135 + -0.08333333335

Combine like terms: -0.343592135 + -0.08333333335 = -0.42692546835
c = -0.42692546835

Simplifying
c = -0.42692546835

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.26025880165, -0.42692546835}