Solve for z 3(5z-3)-4(2z+1)=5z-2

$3 (5 z - 3) - 4 (2 z + 1) = 5 z - 2$

Step 1

Simplify $3 (5 z - 3) - 4 (2 z + 1)$ .

Simplify each term.

Apply the distributive property.

$3 (5 z) + 3 \cdot - 3 - 4 (2 z + 1) = 5 z - 2$

Multiply $5$ by $3$ .

$15 z + 3 \cdot - 3 - 4 (2 z + 1) = 5 z - 2$

Multiply $3$ by $- 3$ .

$15 z - 9 - 4 (2 z + 1) = 5 z - 2$

Apply the distributive property.

$15 z - 9 - 4 (2 z) - 4 \cdot 1 = 5 z - 2$

Multiply $2$ by $- 4$ .

$15 z - 9 - 8 z - 4 \cdot 1 = 5 z - 2$

Multiply $- 4$ by $1$ .

$15 z - 9 - 8 z - 4 = 5 z - 2$

Simplify by adding terms.

Subtract $8 z$ from $15 z$ .

$7 z - 9 - 4 = 5 z - 2$

Subtract $4$ from $- 9$ .

$7 z - 13 = 5 z - 2$

Step 2

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

Subtract $5 z$ from both sides of the equation.

$7 z - 13 - 5 z = - 2$

Subtract $5 z$ from $7 z$ .

$2 z - 13 = - 2$

Step 3

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

Add $13$ to both sides of the equation.

$2 z = - 2 + 13$

Add $- 2$ and $13$ .

$2 z = 11$

Step 4

Divide each term in $2 z = 11$ by $2$ and simplify.

Divide each term in $2 z = 11$ by $2$ .

$\frac{2 z}{2} = \frac{11}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 z}{2} = \frac{11}{2}$

Divide $z$ by $1$ .

$z = \frac{11}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = \frac{11}{2}$

Decimal Form:

$z = 5.5$

Mixed Number Form:

$z = 5 \frac{1}{2}$

Solve for z 3(5z-3)-4(2z+1)=5z-2

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