1(3c)=c(2+c)

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

Simplifying
1(3c) = c(2 + c)

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

Multiply 1 * 3
3c = c(2 + c)
3c = (2 * c + c * c)
3c = (2c + c2)

Solving
3c = 2c + c2

Solving for variable 'c'.

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

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

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

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

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

Subproblem 1
Set the factor 'c' equal to zero and attempt to solve:

Simplifying
c = 0

Solving
c = 0

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

Simplifying
c = 0
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 = {0, 1}