9c(c-11)+10(c+5)+c(6c-3)-30=

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Solution for 9c(c-11)+10(c+5)+c(6c-3)-30= equation: 


Simplifying
9c(c + -11) + 10(c + 5) + c(6c + -3) + -30 = 0

Reorder the terms:
9c(-11 + c) + 10(c + 5) + c(6c + -3) + -30 = 0
(-11 * 9c + c * 9c) + 10(c + 5) + c(6c + -3) + -30 = 0
(-99c + 9c2) + 10(c + 5) + c(6c + -3) + -30 = 0

Reorder the terms:
-99c + 9c2 + 10(5 + c) + c(6c + -3) + -30 = 0
-99c + 9c2 + (5 * 10 + c * 10) + c(6c + -3) + -30 = 0
-99c + 9c2 + (50 + 10c) + c(6c + -3) + -30 = 0

Reorder the terms:
-99c + 9c2 + 50 + 10c + c(-3 + 6c) + -30 = 0
-99c + 9c2 + 50 + 10c + (-3 * c + 6c * c) + -30 = 0
-99c + 9c2 + 50 + 10c + (-3c + 6c2) + -30 = 0

Reorder the terms:
50 + -30 + -99c + 10c + -3c + 9c2 + 6c2 = 0

Combine like terms: 50 + -30 = 20
20 + -99c + 10c + -3c + 9c2 + 6c2 = 0

Combine like terms: -99c + 10c = -89c
20 + -89c + -3c + 9c2 + 6c2 = 0

Combine like terms: -89c + -3c = -92c
20 + -92c + 9c2 + 6c2 = 0

Combine like terms: 9c2 + 6c2 = 15c2
20 + -92c + 15c2 = 0

Solving
20 + -92c + 15c2 = 0

Solving for variable 'c'.

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

Divide each side by '15'.
1.333333333 + -6.133333333c + c2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -6.133333333c + -1.333333333 + c2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -6.133333333c + c2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -6.133333333c + c2 = 0 + -1.333333333
-6.133333333c + c2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-6.133333333c + c2 = -1.333333333

The c term is -6.133333333c.  Take half its coefficient (-3.066666667).
Square it (9.404444446) and add it to both sides.

Add '9.404444446' to each side of the equation.
-6.133333333c + 9.404444446 + c2 = -1.333333333 + 9.404444446

Reorder the terms:
9.404444446 + -6.133333333c + c2 = -1.333333333 + 9.404444446

Combine like terms: -1.333333333 + 9.404444446 = 8.071111113
9.404444446 + -6.133333333c + c2 = 8.071111113

Factor a perfect square on the left side:
(c + -3.066666667)(c + -3.066666667) = 8.071111113

Calculate the square root of the right side: 2.840970101

Break this problem into two subproblems by setting 
(c + -3.066666667) equal to 2.840970101 and -2.840970101.


Subproblem 1
c + -3.066666667 = 2.840970101

Simplifying
c + -3.066666667 = 2.840970101

Reorder the terms:
-3.066666667 + c = 2.840970101

Solving
-3.066666667 + c = 2.840970101

Solving for variable 'c'.

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

Add '3.066666667' to each side of the equation.
-3.066666667 + 3.066666667 + c = 2.840970101 + 3.066666667

Combine like terms: -3.066666667 + 3.066666667 = 0.000000000
0.000000000 + c = 2.840970101 + 3.066666667
c = 2.840970101 + 3.066666667

Combine like terms: 2.840970101 + 3.066666667 = 5.907636768
c = 5.907636768

Simplifying
c = 5.907636768


Subproblem 2
c + -3.066666667 = -2.840970101

Simplifying
c + -3.066666667 = -2.840970101

Reorder the terms:
-3.066666667 + c = -2.840970101

Solving
-3.066666667 + c = -2.840970101

Solving for variable 'c'.

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

Add '3.066666667' to each side of the equation.
-3.066666667 + 3.066666667 + c = -2.840970101 + 3.066666667

Combine like terms: -3.066666667 + 3.066666667 = 0.000000000
0.000000000 + c = -2.840970101 + 3.066666667
c = -2.840970101 + 3.066666667

Combine like terms: -2.840970101 + 3.066666667 = 0.225696566
c = 0.225696566

Simplifying
c = 0.225696566


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {5.907636768, 0.225696566}

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