Algebra Examples

$3 i (2 + 5 i) = x + 6 i$

Step 1

Rewrite the equation as $x + 6 i = 3 i (2 + 5 i)$ .

$x + 6 i = 3 i (2 + 5 i)$

Step 2

Simplify $3 i (2 + 5 i)$ .

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Step 2.1

Rewrite.

$x + 6 i = 0 + 0 + 3 i (2 + 5 i)$

Step 2.2

Simplify by adding zeros.

$x + 6 i = 3 i (2 + 5 i)$

Step 2.3

Apply the distributive property.

$x + 6 i = 3 i \cdot 2 + 3 i (5 i)$

Step 2.4

Multiply $2$ by $3$ .

$x + 6 i = 6 i + 3 i (5 i)$

Step 2.5

Multiply $3 i (5 i)$ .

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Step 2.5.1

Multiply $5$ by $3$ .

$x + 6 i = 6 i + 15 i i$

Step 2.5.2

Raise $i$ to the power of $1$ .

$x + 6 i = 6 i + 15 (i^{1} i)$

Step 2.5.3

Raise $i$ to the power of $1$ .

$x + 6 i = 6 i + 15 (i^{1} i^{1})$

Step 2.5.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x + 6 i = 6 i + 15 i^{1 + 1}$

Step 2.5.5

Add $1$ and $1$ .

$x + 6 i = 6 i + 15 i^{2}$

Step 2.6

Simplify each term.

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Step 2.6.1

Rewrite $i^{2}$ as $- 1$ .

$x + 6 i = 6 i + 15 \cdot - 1$

Step 2.6.2

Multiply $15$ by $- 1$ .

$x + 6 i = 6 i - 15$

Step 2.7

Reorder $6 i$ and $- 15$ .

$x + 6 i = - 15 + 6 i$

Step 3

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

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Step 3.1

Subtract $6 i$ from both sides of the equation.

$x = - 15 + 6 i - 6 i$

Step 3.2

Subtract $6 i$ from $6 i$ .

$x = - 15 + 0$

Step 3.3

Add $- 15$ and $0$ .

$x = - 15$