(4c-4)-(c-3)c=2

Solution for (4c-4)-(c-3)c=2 equation:

Simplifying
(4c + -4) + -1(c + -3) * c = 2

Reorder the terms:
(-4 + 4c) + -1(c + -3) * c = 2

Remove parenthesis around (-4 + 4c)
-4 + 4c + -1(c + -3) * c = 2

Reorder the terms:
-4 + 4c + -1(-3 + c) * c = 2

Reorder the terms for easier multiplication:
-4 + 4c + -1c(-3 + c) = 2
-4 + 4c + (-3 * -1c + c * -1c) = 2
-4 + 4c + (3c + -1c2) = 2

Combine like terms: 4c + 3c = 7c
-4 + 7c + -1c2 = 2

Solving
-4 + 7c + -1c2 = 2

Solving for variable 'c'.

Reorder the terms:
-4 + -2 + 7c + -1c2 = 2 + -2

Combine like terms: -4 + -2 = -6
-6 + 7c + -1c2 = 2 + -2

Combine like terms: 2 + -2 = 0
-6 + 7c + -1c2 = 0

Factor a trinomial.
(-6 + c)(1 + -1c) = 0

Subproblem 1
Set the factor '(-6 + c)' equal to zero and attempt to solve:

Simplifying
-6 + c = 0

Solving
-6 + c = 0

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

Add '6' to each side of the equation.
-6 + 6 + c = 0 + 6

Combine like terms: -6 + 6 = 0
0 + c = 0 + 6
c = 0 + 6

Combine like terms: 0 + 6 = 6
c = 6

Simplifying
c = 6
Subproblem 2
Set the factor '(1 + -1c)' equal to zero and attempt to solve:

Simplifying
1 + -1c = 0

Solving
1 + -1c = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1c = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1c = 0 + -1
-1c = 0 + -1

Combine like terms: 0 + -1 = -1
-1c = -1

Divide each side by '-1'.
c = 1

Simplifying
c = 1
Solution
c = {6, 1}