Basic Math Examples

$5 (3 (z + 4) - 2 (1 - z)) - z - 15 = 14 z$

Step 1

Simplify $5 (3 (z + 4) - 2 (1 - z)) - z - 15$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$5 (3 z + 3 \cdot 4 - 2 (1 - z)) - z - 15 = 14 z$

Step 1.1.1.2

Multiply $3$ by $4$ .

$5 (3 z + 12 - 2 (1 - z)) - z - 15 = 14 z$

Step 1.1.1.3

Apply the distributive property.

$5 (3 z + 12 - 2 \cdot 1 - 2 (- z)) - z - 15 = 14 z$

Step 1.1.1.4

Multiply $- 2$ by $1$ .

$5 (3 z + 12 - 2 - 2 (- z)) - z - 15 = 14 z$

Step 1.1.1.5

Multiply $- 1$ by $- 2$ .

$5 (3 z + 12 - 2 + 2 z) - z - 15 = 14 z$

$5 (3 z + 12 - 2 + 2 z) - z - 15 = 14 z$

Step 1.1.2

Add $3 z$ and $2 z$ .

$5 (5 z + 12 - 2) - z - 15 = 14 z$

Step 1.1.3

Subtract $2$ from $12$ .

$5 (5 z + 10) - z - 15 = 14 z$

Step 1.1.4

Apply the distributive property.

$5 (5 z) + 5 \cdot 10 - z - 15 = 14 z$

Step 1.1.5

Multiply $5$ by $5$ .

$25 z + 5 \cdot 10 - z - 15 = 14 z$

Step 1.1.6

Multiply $5$ by $10$ .

$25 z + 50 - z - 15 = 14 z$

$25 z + 50 - z - 15 = 14 z$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $z$ from $25 z$ .

$24 z + 50 - 15 = 14 z$

Step 1.2.2

Subtract $15$ from $50$ .

$24 z + 35 = 14 z$

$24 z + 35 = 14 z$

$24 z + 35 = 14 z$

Step 2

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

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Step 2.1

Subtract $14 z$ from both sides of the equation.

$24 z + 35 - 14 z = 0$

Step 2.2

Subtract $14 z$ from $24 z$ .

$10 z + 35 = 0$

$10 z + 35 = 0$

Step 3

Subtract $35$ from both sides of the equation.

$10 z = - 35$

Step 4

Divide each term in $10 z = - 35$ by $10$ and simplify.

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Step 4.1

Divide each term in $10 z = - 35$ by $10$ .

$\frac{10 z}{10} = \frac{- 35}{10}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $10$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{10 z}{10} = \frac{- 35}{10}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 35}{10}$

$z = \frac{- 35}{10}$

$z = \frac{- 35}{10}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 35$ and $10$ .

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Step 4.3.1.1

Factor $5$ out of $- 35$ .

$z = \frac{5 (- 7)}{10}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $5$ out of $10$ .

$z = \frac{5 \cdot - 7}{5 \cdot 2}$

Step 4.3.1.2.2

Cancel the common factor.

$z = \frac{5 \cdot - 7}{5 \cdot 2}$

Step 4.3.1.2.3

Rewrite the expression.

$z = \frac{- 7}{2}$

$z = \frac{- 7}{2}$

$z = \frac{- 7}{2}$

Step 4.3.2

Move the negative in front of the fraction.

$z = - \frac{7}{2}$

$z = - \frac{7}{2}$

$z = - \frac{7}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = - \frac{7}{2}$

Decimal Form:

$z = - 3.5$

Mixed Number Form:

$z = - 3 \frac{1}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$