(3c-8)(c-1)=(2c+1)(c+6)

Solution for (3c-8)(c-1)=(2c+1)(c+6) equation:

Simplifying
(3c + -8)(c + -1) = (2c + 1)(c + 6)

Reorder the terms:
(-8 + 3c)(c + -1) = (2c + 1)(c + 6)

Reorder the terms:
(-8 + 3c)(-1 + c) = (2c + 1)(c + 6)

Multiply (-8 + 3c) * (-1 + c)
(-8(-1 + c) + 3c * (-1 + c)) = (2c + 1)(c + 6)
((-1 * -8 + c * -8) + 3c * (-1 + c)) = (2c + 1)(c + 6)
((8 + -8c) + 3c * (-1 + c)) = (2c + 1)(c + 6)
(8 + -8c + (-1 * 3c + c * 3c)) = (2c + 1)(c + 6)
(8 + -8c + (-3c + 3c2)) = (2c + 1)(c + 6)

Combine like terms: -8c + -3c = -11c
(8 + -11c + 3c2) = (2c + 1)(c + 6)

Reorder the terms:
8 + -11c + 3c2 = (1 + 2c)(c + 6)

Reorder the terms:
8 + -11c + 3c2 = (1 + 2c)(6 + c)

Multiply (1 + 2c) * (6 + c)
8 + -11c + 3c2 = (1(6 + c) + 2c * (6 + c))
8 + -11c + 3c2 = ((6 * 1 + c * 1) + 2c * (6 + c))
8 + -11c + 3c2 = ((6 + 1c) + 2c * (6 + c))
8 + -11c + 3c2 = (6 + 1c + (6 * 2c + c * 2c))
8 + -11c + 3c2 = (6 + 1c + (12c + 2c2))

Combine like terms: 1c + 12c = 13c
8 + -11c + 3c2 = (6 + 13c + 2c2)

Solving
8 + -11c + 3c2 = 6 + 13c + 2c2

Solving for variable 'c'.

Reorder the terms:
8 + -6 + -11c + -13c + 3c2 + -2c2 = 6 + 13c + 2c2 + -6 + -13c + -2c2

Combine like terms: 8 + -6 = 2
2 + -11c + -13c + 3c2 + -2c2 = 6 + 13c + 2c2 + -6 + -13c + -2c2

Combine like terms: -11c + -13c = -24c
2 + -24c + 3c2 + -2c2 = 6 + 13c + 2c2 + -6 + -13c + -2c2

Combine like terms: 3c2 + -2c2 = 1c2
2 + -24c + 1c2 = 6 + 13c + 2c2 + -6 + -13c + -2c2

Reorder the terms:
2 + -24c + 1c2 = 6 + -6 + 13c + -13c + 2c2 + -2c2

Combine like terms: 6 + -6 = 0
2 + -24c + 1c2 = 0 + 13c + -13c + 2c2 + -2c2
2 + -24c + 1c2 = 13c + -13c + 2c2 + -2c2

Combine like terms: 13c + -13c = 0
2 + -24c + 1c2 = 0 + 2c2 + -2c2
2 + -24c + 1c2 = 2c2 + -2c2

Combine like terms: 2c2 + -2c2 = 0
2 + -24c + 1c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -24c + -2 + c2 = 0 + -2

Reorder the terms:
2 + -2 + -24c + c2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -24c + c2 = 0 + -2
-24c + c2 = 0 + -2

Combine like terms: 0 + -2 = -2
-24c + c2 = -2

The c term is -24c.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24c + 144 + c2 = -2 + 144

Reorder the terms:
144 + -24c + c2 = -2 + 144

Combine like terms: -2 + 144 = 142
144 + -24c + c2 = 142

Factor a perfect square on the left side:
(c + -12)(c + -12) = 142

Calculate the square root of the right side: 11.916375288

Break this problem into two subproblems by setting 
(c + -12) equal to 11.916375288 and -11.916375288.

Subproblem 1
c + -12 = 11.916375288

Simplifying
c + -12 = 11.916375288

Reorder the terms:
-12 + c = 11.916375288

Solving
-12 + c = 11.916375288

Solving for variable 'c'.

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

Add '12' to each side of the equation.
-12 + 12 + c = 11.916375288 + 12

Combine like terms: -12 + 12 = 0
0 + c = 11.916375288 + 12
c = 11.916375288 + 12

Combine like terms: 11.916375288 + 12 = 23.916375288
c = 23.916375288

Simplifying
c = 23.916375288

Subproblem 2
c + -12 = -11.916375288

Simplifying
c + -12 = -11.916375288

Reorder the terms:
-12 + c = -11.916375288

Solving
-12 + c = -11.916375288

Solving for variable 'c'.

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

Add '12' to each side of the equation.
-12 + 12 + c = -11.916375288 + 12

Combine like terms: -12 + 12 = 0
0 + c = -11.916375288 + 12
c = -11.916375288 + 12

Combine like terms: -11.916375288 + 12 = 0.083624712
c = 0.083624712

Simplifying
c = 0.083624712

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {23.916375288, 0.083624712}