Solve for z 2(4z-1)=3(z+2)

$2 (4 z - 1) = 3 (z + 2)$

Step 1

Simplify $2 (4 z - 1)$ .

Start simplifying.

$0 + 0 + 2 (4 z - 1) = 3 (z + 2)$

Simplify by adding zeros.

$2 (4 z - 1) = 3 (z + 2)$

Apply the distributive property.

$2 (4 z) + 2 \cdot - 1 = 3 (z + 2)$

Multiply.

Multiply $4$ by $2$ .

$8 z + 2 \cdot - 1 = 3 (z + 2)$

Multiply $2$ by $- 1$ .

$8 z - 2 = 3 (z + 2)$

Step 2

Simplify $3 (z + 2)$ .

Apply the distributive property.

$8 z - 2 = 3 z + 3 \cdot 2$

Multiply $3$ by $2$ .

$8 z - 2 = 3 z + 6$

Step 3

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

Subtract $3 z$ from both sides of the equation.

$8 z - 2 - 3 z = 6$

Subtract $3 z$ from $8 z$ .

$5 z - 2 = 6$

Step 4

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

Add $2$ to both sides of the equation.

$5 z = 6 + 2$

Add $6$ and $2$ .

$5 z = 8$

Step 5

Divide each term in $5 z = 8$ by $5$ and simplify.

Divide each term in $5 z = 8$ by $5$ .

$\frac{5 z}{5} = \frac{8}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 z}{5} = \frac{8}{5}$

Divide $z$ by $1$ .

$z = \frac{8}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$z = \frac{8}{5}$

Decimal Form:

$z = 1.6$

Mixed Number Form:

$z = 1 \frac{3}{5}$

Solve for z 2(4z-1)=3(z+2)

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