Solve for x 12-5x-4kx=y

$12 - 5 x - 4 k x = y$

Step 1

Subtract $12$ from both sides of the equation.

$- 5 x - 4 k x = y - 12$

Step 2

Factor $x$ out of $- 5 x - 4 k x$ .

Factor $x$ out of $- 5 x$ .

$x \cdot - 5 - 4 k x = y - 12$

Factor $x$ out of $- 4 k x$ .

$x \cdot - 5 + x (- 4 k) = y - 12$

Factor $x$ out of $x \cdot - 5 + x (- 4 k)$ .

$x (- 5 - 4 k) = y - 12$

Step 3

Divide each term in $x (- 5 - 4 k) = y - 12$ by $- 5 - 4 k$ and simplify.

Divide each term in $x (- 5 - 4 k) = y - 12$ by $- 5 - 4 k$ .

$\frac{x (- 5 - 4 k)}{- 5 - 4 k} = \frac{y}{- 5 - 4 k} + \frac{- 12}{- 5 - 4 k}$

Simplify the left side.

Cancel the common factor of $- 5 - 4 k$ .

Cancel the common factor.

$\frac{x (- 5 - 4 k)}{- 5 - 4 k} = \frac{y}{- 5 - 4 k} + \frac{- 12}{- 5 - 4 k}$

Divide $x$ by $1$ .

$x = \frac{y}{- 5 - 4 k} + \frac{- 12}{- 5 - 4 k}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{y - 12}{- 5 - 4 k}$

Rewrite $- 5$ as $- 1 (5)$ .

$x = \frac{y - 12}{- 1 (5) - 4 k}$

Factor $- 1$ out of $- 4 k$ .

$x = \frac{y - 12}{- 1 (5) - (4 k)}$

Factor $- 1$ out of $- 1 (5) - (4 k)$ .

$x = \frac{y - 12}{- 1 (5 + 4 k)}$

Move the negative in front of the fraction.

$x = - \frac{y - 12}{5 + 4 k}$