Solve for c 2/3c-2=2+c

$\frac{2}{3} c - 2 = 2 + c$

Combine $\frac{2}{3}$ and $c$ .

$\frac{2 c}{3} - 2 = 2 + c$

Move all terms containing $c$ to the left side of the equation.

Subtract $c$ from both sides of the equation.

$\frac{2 c}{3} - 2 - c = 2$

To write $- c$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 c}{3} - c \cdot \frac{3}{3} - 2 = 2$

Combine $- c$ and $\frac{3}{3}$ .

$\frac{2 c}{3} + \frac{- c \cdot 3}{3} - 2 = 2$

Combine the numerators over the common denominator.

$\frac{2 c - c \cdot 3}{3} - 2 = 2$

Simplify each term.

Simplify the numerator.

Factor $c$ out of $2 c - c \cdot 3$ .

Factor $c$ out of $2 c$ .

$\frac{c \cdot 2 - c \cdot 3}{3} - 2 = 2$

Factor $c$ out of $- c \cdot 3$ .

$\frac{c \cdot 2 + c (- 1 \cdot 3)}{3} - 2 = 2$

Factor $c$ out of $c \cdot 2 + c (- 1 \cdot 3)$ .

$\frac{c (2 - 1 \cdot 3)}{3} - 2 = 2$

Multiply $- 1$ by $3$ .

$\frac{c (2 - 3)}{3} - 2 = 2$

Subtract $3$ from $2$ .

$\frac{c \cdot - 1}{3} - 2 = 2$

Move $- 1$ to the left of $c$ .

$\frac{- 1 \cdot c}{3} - 2 = 2$

Move the negative in front of the fraction.

$- \frac{c}{3} - 2 = 2$

Move all terms not containing $c$ to the right side of the equation.

Add $2$ to both sides of the equation.

$- \frac{c}{3} = 2 + 2$

Add $2$ and $2$ .

$- \frac{c}{3} = 4$

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{c}{3}) = - 3 \cdot 4$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{c}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{c}{3}$ into the numerator.

$- 3 \frac{- c}{3} = - 3 \cdot 4$

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- c}{3} = - 3 \cdot 4$

Cancel the common factor.

$3 \cdot - 1 \frac{- c}{3} = - 3 \cdot 4$

Rewrite the expression.

$- - c = - 3 \cdot 4$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 c = - 3 \cdot 4$

Multiply $c$ by $1$ .

$c = - 3 \cdot 4$

Simplify the right side.

Multiply $- 3$ by $4$ .

$c = - 12$

Solve for c 2/3c-2=2+c

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