Solve for x x-1=6(5x-2)

$x - 1 = 6 (5 x - 2)$

Simplify $6 (5 x - 2)$ .

Rewrite.

$x - 1 = 0 + 0 + 6 (5 x - 2)$

Simplify by adding zeros.

$x - 1 = 6 (5 x - 2)$

Apply the distributive property.

$x - 1 = 6 (5 x) + 6 \cdot - 2$

Multiply.

Multiply $5$ by $6$ .

$x - 1 = 30 x + 6 \cdot - 2$

Multiply $6$ by $- 2$ .

$x - 1 = 30 x - 12$

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

Subtract $30 x$ from both sides of the equation.

$x - 1 - 30 x = - 12$

Subtract $30 x$ from $x$ .

$- 29 x - 1 = - 12$

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

Add $1$ to both sides of the equation.

$- 29 x = - 12 + 1$

Add $- 12$ and $1$ .

$- 29 x = - 11$

Divide each term in $- 29 x = - 11$ by $- 29$ and simplify.

Divide each term in $- 29 x = - 11$ by $- 29$ .

$\frac{- 29 x}{- 29} = \frac{- 11}{- 29}$

Simplify the left side.

Cancel the common factor of $- 29$ .

Cancel the common factor.

$\frac{- 29 x}{- 29} = \frac{- 11}{- 29}$

Divide $x$ by $1$ .

$x = \frac{- 11}{- 29}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{11}{29}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{29}$

Decimal Form:

$x = 0.37931034 \dots$