Basic Math Examples

$3 (3 z - 15) = 9 (z - 5)$

Step 1

Simplify $3 (3 z - 15)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (3 z - 15) = 9 (z - 5)$

Step 1.2

Simplify by adding zeros.

$3 (3 z - 15) = 9 (z - 5)$

Step 1.3

Apply the distributive property.

$3 (3 z) + 3 \cdot - 15 = 9 (z - 5)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $3$ .

$9 z + 3 \cdot - 15 = 9 (z - 5)$

Step 1.4.2

Multiply $3$ by $- 15$ .

$9 z - 45 = 9 (z - 5)$

Step 2

Simplify $9 (z - 5)$ .

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Step 2.1

Apply the distributive property.

$9 z - 45 = 9 z + 9 \cdot - 5$

Step 2.2

Multiply $9$ by $- 5$ .

$9 z - 45 = 9 z - 45$

Step 3

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

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Step 3.1

Subtract $9 z$ from both sides of the equation.

$9 z - 45 - 9 z = - 45$

Step 3.2

Combine the opposite terms in $9 z - 45 - 9 z$ .

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Step 3.2.1

Subtract $9 z$ from $9 z$ .

$0 - 45 = - 45$

Step 3.2.2

Subtract $45$ from $0$ .

$- 45 = - 45$

Step 4

Since $- 45 = - 45$ , the equation will always be true for any value of $z$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$