Solve for z z+3(z+7)=-5

$z + 3 (z + 7) = - 5$

Step 1

Simplify $z + 3 (z + 7)$ .

Simplify each term.

Apply the distributive property.

$z + 3 z + 3 \cdot 7 = - 5$

Multiply $3$ by $7$ .

$z + 3 z + 21 = - 5$

Add $z$ and $3 z$ .

$4 z + 21 = - 5$

Step 2

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

Subtract $21$ from both sides of the equation.

$4 z = - 5 - 21$

Subtract $21$ from $- 5$ .

$4 z = - 26$

Step 3

Divide each term in $4 z = - 26$ by $4$ and simplify.

Divide each term in $4 z = - 26$ by $4$ .

$\frac{4 z}{4} = \frac{- 26}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 z}{4} = \frac{- 26}{4}$

Divide $z$ by $1$ .

$z = \frac{- 26}{4}$

Simplify the right side.

Cancel the common factor of $- 26$ and $4$ .

Factor $2$ out of $- 26$ .

$z = \frac{2 (- 13)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$z = \frac{2 \cdot - 13}{2 \cdot 2}$

Cancel the common factor.

$z = \frac{2 \cdot - 13}{2 \cdot 2}$

Rewrite the expression.

$z = \frac{- 13}{2}$

Move the negative in front of the fraction.

$z = - \frac{13}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{13}{2}$

Decimal Form:

$z = - 6.5$

Mixed Number Form:

$z = - 6 \frac{1}{2}$

Solve for z z+3(z+7)=-5

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