Algebra Examples

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

Step 1

Subtract $12$ from both sides of the equation.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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.

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $x$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Combine the numerators over the common denominator.

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

Step 3.3.2

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

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

Step 3.3.3

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

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

Step 3.3.4

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

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

Step 3.3.5

Move the negative in front of the fraction.

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