Simplify 5x(2-3x)+4(2-3x)+2-3x

$5 x (2 - 3 x) + 4 (2 - 3 x) + 2 - 3 x$

Simplify each term.

Apply the distributive property.

$5 x \cdot 2 + 5 x (- 3 x) + 4 (2 - 3 x) + 2 - 3 x$

Multiply $2$ by $5$ .

$10 x + 5 x (- 3 x) + 4 (2 - 3 x) + 2 - 3 x$

Rewrite using the commutative property of multiplication.

$10 x + 5 \cdot - 3 x \cdot x + 4 (2 - 3 x) + 2 - 3 x$

Simplify each term.

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

Move $x$ .

$10 x + 5 \cdot - 3 (x \cdot x) + 4 (2 - 3 x) + 2 - 3 x$

Multiply $x$ by $x$ .

$10 x + 5 \cdot - 3 x^{2} + 4 (2 - 3 x) + 2 - 3 x$

Multiply $5$ by $- 3$ .

$10 x - 15 x^{2} + 4 (2 - 3 x) + 2 - 3 x$

Apply the distributive property.

$10 x - 15 x^{2} + 4 \cdot 2 + 4 (- 3 x) + 2 - 3 x$

Multiply $4$ by $2$ .

$10 x - 15 x^{2} + 8 + 4 (- 3 x) + 2 - 3 x$

Multiply $- 3$ by $4$ .

$10 x - 15 x^{2} + 8 - 12 x + 2 - 3 x$

Simplify by adding terms.

Subtract $12 x$ from $10 x$ .

$- 2 x - 15 x^{2} + 8 + 2 - 3 x$

Subtract $3 x$ from $- 2 x$ .

$- 5 x - 15 x^{2} + 8 + 2$

Simplify the expression.

Add $8$ and $2$ .

$- 5 x - 15 x^{2} + 10$

Reorder $- 5 x$ and $- 15 x^{2}$ .

$- 15 x^{2} - 5 x + 10$