Solve for c c÷(4-3c)-2=0

$c \div (4 - 3 c) - 2 = 0$

Step 1

Simplify $c \div (4 - 3 c) - 2$ .

Rewrite the division as a fraction.

$\frac{c}{4 - 3 c} - 2 = 0$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4 - 3 c}{4 - 3 c}$ .

$\frac{c}{4 - 3 c} - 2 \cdot \frac{4 - 3 c}{4 - 3 c} = 0$

Simplify terms.

Combine $- 2$ and $\frac{4 - 3 c}{4 - 3 c}$ .

$\frac{c}{4 - 3 c} + \frac{- 2 (4 - 3 c)}{4 - 3 c} = 0$

Combine the numerators over the common denominator.

$\frac{c - 2 (4 - 3 c)}{4 - 3 c} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{c - 2 \cdot 4 - 2 (- 3 c)}{4 - 3 c} = 0$

Multiply $- 2$ by $4$ .

$\frac{c - 8 - 2 (- 3 c)}{4 - 3 c} = 0$

Multiply $- 3$ by $- 2$ .

$\frac{c - 8 + 6 c}{4 - 3 c} = 0$

Add $c$ and $6 c$ .

$\frac{7 c - 8}{4 - 3 c} = 0$

Step 2

Set the numerator equal to zero.

$7 c - 8 = 0$

Step 3

Solve the equation for $c$ .

Add $8$ to both sides of the equation.

$7 c = 8$

Divide each term in $7 c = 8$ by $7$ and simplify.

Divide each term in $7 c = 8$ by $7$ .

$\frac{7 c}{7} = \frac{8}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 c}{7} = \frac{8}{7}$

Divide $c$ by $1$ .

$c = \frac{8}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = \frac{8}{7}$

Decimal Form:

$c = 1.\overline{142857}$

Mixed Number Form:

$c = 1 \frac{1}{7}$