Simplify 2(4x^2-2x)-3(-6x^2+4)+2x(x-1)

$2 (4 x^{2} - 2 x) - 3 (- 6 x^{2} + 4) + 2 x (x - 1)$

Simplify each term.

Apply the distributive property.

$2 (4 x^{2}) + 2 (- 2 x) - 3 (- 6 x^{2} + 4) + 2 x (x - 1)$

Multiply $4$ by $2$ .

$8 x^{2} + 2 (- 2 x) - 3 (- 6 x^{2} + 4) + 2 x (x - 1)$

Multiply $- 2$ by $2$ .

$8 x^{2} - 4 x - 3 (- 6 x^{2} + 4) + 2 x (x - 1)$

Apply the distributive property.

$8 x^{2} - 4 x - 3 (- 6 x^{2}) - 3 \cdot 4 + 2 x (x - 1)$

Multiply $- 6$ by $- 3$ .

$8 x^{2} - 4 x + 18 x^{2} - 3 \cdot 4 + 2 x (x - 1)$

Multiply $- 3$ by $4$ .

$8 x^{2} - 4 x + 18 x^{2} - 12 + 2 x (x - 1)$

Apply the distributive property.

$8 x^{2} - 4 x + 18 x^{2} - 12 + 2 x \cdot x + 2 x \cdot - 1$

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

Move $x$ .

$8 x^{2} - 4 x + 18 x^{2} - 12 + 2 (x \cdot x) + 2 x \cdot - 1$

Multiply $x$ by $x$ .

$8 x^{2} - 4 x + 18 x^{2} - 12 + 2 x^{2} + 2 x \cdot - 1$

Multiply $- 1$ by $2$ .

$8 x^{2} - 4 x + 18 x^{2} - 12 + 2 x^{2} - 2 x$

Simplify by adding terms.

Add $8 x^{2}$ and $18 x^{2}$ .

$26 x^{2} - 4 x - 12 + 2 x^{2} - 2 x$

Add $26 x^{2}$ and $2 x^{2}$ .

$28 x^{2} - 4 x - 12 - 2 x$

Subtract $2 x$ from $- 4 x$ .

$28 x^{2} - 6 x - 12$