3c(c-6)-2c(c-1)=5c^2-15+20

Solution for 3c(c-6)-2c(c-1)=5c^2-15+20 equation:

Simplifying
3c(c + -6) + -2c(c + -1) = 5c2 + -15 + 20

Reorder the terms:
3c(-6 + c) + -2c(c + -1) = 5c2 + -15 + 20
(-6 * 3c + c * 3c) + -2c(c + -1) = 5c2 + -15 + 20
(-18c + 3c2) + -2c(c + -1) = 5c2 + -15 + 20

Reorder the terms:
-18c + 3c2 + -2c(-1 + c) = 5c2 + -15 + 20
-18c + 3c2 + (-1 * -2c + c * -2c) = 5c2 + -15 + 20
-18c + 3c2 + (2c + -2c2) = 5c2 + -15 + 20

Reorder the terms:
-18c + 2c + 3c2 + -2c2 = 5c2 + -15 + 20

Combine like terms: -18c + 2c = -16c
-16c + 3c2 + -2c2 = 5c2 + -15 + 20

Combine like terms: 3c2 + -2c2 = 1c2
-16c + 1c2 = 5c2 + -15 + 20

Reorder the terms:
-16c + 1c2 = -15 + 20 + 5c2

Combine like terms: -15 + 20 = 5
-16c + 1c2 = 5 + 5c2

Solving
-16c + 1c2 = 5 + 5c2

Solving for variable 'c'.

Reorder the terms:
-5 + -16c + 1c2 + -5c2 = 5 + 5c2 + -5 + -5c2

Combine like terms: 1c2 + -5c2 = -4c2
-5 + -16c + -4c2 = 5 + 5c2 + -5 + -5c2

Reorder the terms:
-5 + -16c + -4c2 = 5 + -5 + 5c2 + -5c2

Combine like terms: 5 + -5 = 0
-5 + -16c + -4c2 = 0 + 5c2 + -5c2
-5 + -16c + -4c2 = 5c2 + -5c2

Combine like terms: 5c2 + -5c2 = 0
-5 + -16c + -4c2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 16c + 4c2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 16c + 4c2)' equal to zero and attempt to solve:

Simplifying
5 + 16c + 4c2 = 0

Solving
5 + 16c + 4c2 = 0

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

Divide each side by '4'.
1.25 + 4c + c2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 4c + -1.25 + c2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 4c + c2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 4c + c2 = 0 + -1.25
4c + c2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
4c + c2 = -1.25

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 = -1.25 + 4

Reorder the terms:
4 + 4c + c2 = -1.25 + 4

Combine like terms: -1.25 + 4 = 2.75
4 + 4c + c2 = 2.75

Factor a perfect square on the left side:
(c + 2)(c + 2) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(c + 2) equal to 1.658312395 and -1.658312395.

Subproblem 1
c + 2 = 1.658312395

Simplifying
c + 2 = 1.658312395

Reorder the terms:
2 + c = 1.658312395

Solving
2 + c = 1.658312395

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 = 1.658312395 + -2

Combine like terms: 2 + -2 = 0
0 + c = 1.658312395 + -2
c = 1.658312395 + -2

Combine like terms: 1.658312395 + -2 = -0.341687605
c = -0.341687605

Simplifying
c = -0.341687605

Subproblem 2
c + 2 = -1.658312395

Simplifying
c + 2 = -1.658312395

Reorder the terms:
2 + c = -1.658312395

Solving
2 + c = -1.658312395

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 = -1.658312395 + -2

Combine like terms: 2 + -2 = 0
0 + c = -1.658312395 + -2
c = -1.658312395 + -2

Combine like terms: -1.658312395 + -2 = -3.658312395
c = -3.658312395

Simplifying
c = -3.658312395

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.341687605, -3.658312395}
Solution
c = {-0.341687605, -3.658312395}