Solve for x -6(9x+5)-3x+4x=-408+x

$- 6 (9 x + 5) - 3 x + 4 x = - 408 + x$

Step 1

Simplify $- 6 (9 x + 5) - 3 x + 4 x$ .

Simplify each term.

Apply the distributive property.

$- 6 (9 x) - 6 \cdot 5 - 3 x + 4 x = - 408 + x$

Multiply $9$ by $- 6$ .

$- 54 x - 6 \cdot 5 - 3 x + 4 x = - 408 + x$

Multiply $- 6$ by $5$ .

$- 54 x - 30 - 3 x + 4 x = - 408 + x$

Simplify by adding terms.

Subtract $3 x$ from $- 54 x$ .

$- 57 x - 30 + 4 x = - 408 + x$

Add $- 57 x$ and $4 x$ .

$- 53 x - 30 = - 408 + x$

Step 2

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

Subtract $x$ from both sides of the equation.

$- 53 x - 30 - x = - 408$

Subtract $x$ from $- 53 x$ .

$- 54 x - 30 = - 408$

Step 3

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

Add $30$ to both sides of the equation.

$- 54 x = - 408 + 30$

Add $- 408$ and $30$ .

$- 54 x = - 378$

Step 4

Divide each term in $- 54 x = - 378$ by $- 54$ and simplify.

Divide each term in $- 54 x = - 378$ by $- 54$ .

$\frac{- 54 x}{- 54} = \frac{- 378}{- 54}$

Simplify the left side.

Cancel the common factor of $- 54$ .

Cancel the common factor.

$\frac{- 54 x}{- 54} = \frac{- 378}{- 54}$

Divide $x$ by $1$ .

$x = \frac{- 378}{- 54}$

Simplify the right side.

Divide $- 378$ by $- 54$ .

$x = 7$