Solve for x y=4x+rx+6 for x

$y = 4 x + r x + 6$ for $x$

Step 1

Rewrite the equation as $4 x + r x + 6 = y$ .

$4 x + r x + 6 = y$

Step 2

Subtract $6$ from both sides of the equation.

$4 x + r x = y - 6$

Step 3

Factor $x$ out of $4 x + r x$ .

Factor $x$ out of $4 x$ .

$x \cdot 4 + r x = y - 6$

Factor $x$ out of $r x$ .

$x \cdot 4 + x r = y - 6$

Factor $x$ out of $x \cdot 4 + x r$ .

$x (4 + r) = y - 6$

Step 4

Divide each term in $x (4 + r) = y - 6$ by $4 + r$ and simplify.

Divide each term in $x (4 + r) = y - 6$ by $4 + r$ .

$\frac{x (4 + r)}{4 + r} = \frac{y}{4 + r} + \frac{- 6}{4 + r}$

Simplify the left side.

Cancel the common factor of $4 + r$ .

Cancel the common factor.

$\frac{x (4 + r)}{4 + r} = \frac{y}{4 + r} + \frac{- 6}{4 + r}$

Divide $x$ by $1$ .

$x = \frac{y}{4 + r} + \frac{- 6}{4 + r}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{y - 6}{4 + r}$