Simplify (-3x+2i)(x-4i)

$(- 3 x + 2 i) (x - 4 i)$

Expand $(- 3 x + 2 i) (x - 4 i)$ using the FOIL Method.

Apply the distributive property.

$- 3 x (x - 4 i) + 2 i (x - 4 i)$

Apply the distributive property.

$- 3 x \cdot x - 3 x (- 4 i) + 2 i (x - 4 i)$

Apply the distributive property.

$- 3 x \cdot x - 3 x (- 4 i) + 2 i x + 2 i (- 4 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 3 (x \cdot x) - 3 x (- 4 i) + 2 i x + 2 i (- 4 i)$

Multiply $x$ by $x$ .

$- 3 x^{2} - 3 x (- 4 i) + 2 i x + 2 i (- 4 i)$

Multiply $- 4$ by $- 3$ .

$- 3 x^{2} + 12 x i + 2 i x + 2 i (- 4 i)$

Multiply $2 i (- 4 i)$ .

Multiply $- 4$ by $2$ .

$- 3 x^{2} + 12 x i + 2 i x - 8 i i$

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

$- 3 x^{2} + 12 x i + 2 i x - 8 (i^{1} i)$

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

$- 3 x^{2} + 12 x i + 2 i x - 8 (i^{1} i^{1})$

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

$- 3 x^{2} + 12 x i + 2 i x - 8 i^{1 + 1}$

Add $1$ and $1$ .

$- 3 x^{2} + 12 x i + 2 i x - 8 i^{2}$

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

$- 3 x^{2} + 12 x i + 2 i x - 8 \cdot - 1$

Multiply $- 8$ by $- 1$ .

$- 3 x^{2} + 12 x i + 2 i x + 8$

Add $12 x i$ and $2 i x$ .

Move $i$ .

$- 3 x^{2} + 12 x i + 2 x i + 8$

Add $12 x i$ and $2 x i$ .

$- 3 x^{2} + 14 x i + 8$