Solve for z -7(7z-1)=7-4z

$- 7 (7 z - 1) = 7 - 4 z$

Step 1

Simplify $- 7 (7 z - 1)$ .

Rewrite.

$0 + 0 - 7 (7 z - 1) = 7 - 4 z$

Simplify by adding zeros.

$- 7 (7 z - 1) = 7 - 4 z$

Apply the distributive property.

$- 7 (7 z) - 7 \cdot - 1 = 7 - 4 z$

Multiply.

Multiply $7$ by $- 7$ .

$- 49 z - 7 \cdot - 1 = 7 - 4 z$

Multiply $- 7$ by $- 1$ .

$- 49 z + 7 = 7 - 4 z$

Step 2

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

Add $4 z$ to both sides of the equation.

$- 49 z + 7 + 4 z = 7$

Add $- 49 z$ and $4 z$ .

$- 45 z + 7 = 7$

Step 3

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

Subtract $7$ from both sides of the equation.

$- 45 z = 7 - 7$

Subtract $7$ from $7$ .

$- 45 z = 0$

Step 4

Divide each term in $- 45 z = 0$ by $- 45$ and simplify.

Divide each term in $- 45 z = 0$ by $- 45$ .

$\frac{- 45 z}{- 45} = \frac{0}{- 45}$

Simplify the left side.

Cancel the common factor of $- 45$ .

Cancel the common factor.

$\frac{- 45 z}{- 45} = \frac{0}{- 45}$

Divide $z$ by $1$ .

$z = \frac{0}{- 45}$

Simplify the right side.

Divide $0$ by $- 45$ .

$z = 0$