Simplify x(2x+3(x-(3x+1)))

$x (2 x + 3 (x - (3 x + 1)))$

Simplify each term.

Simplify each term.

Apply the distributive property.

$x (2 x + 3 (x - (3 x) - 1 \cdot 1))$

Multiply $3$ by $- 1$ .

$x (2 x + 3 (x - 3 x - 1 \cdot 1))$

Multiply $- 1$ by $1$ .

$x (2 x + 3 (x - 3 x - 1))$

$x (2 x + 3 (x - 3 x - 1))$

Subtract $3 x$ from $x$ .

$x (2 x + 3 (- 2 x - 1))$

Apply the distributive property.

$x (2 x + 3 (- 2 x) + 3 \cdot - 1)$

Multiply $- 2$ by $3$ .

$x (2 x - 6 x + 3 \cdot - 1)$

Multiply $3$ by $- 1$ .

$x (2 x - 6 x - 3)$

$x (2 x - 6 x - 3)$

Simplify terms.

Subtract $6 x$ from $2 x$ .

$x (- 4 x - 3)$

Apply the distributive property.

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

Reorder.

Rewrite using the commutative property of multiplication.

$- 4 x \cdot x + x \cdot - 3$

Move $- 3$ to the left of $x$ .

$- 4 x \cdot x - 3 \cdot x$

$- 4 x \cdot x - 3 \cdot x$

$- 4 x \cdot x - 3 \cdot x$

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

Move $x$ .

$- 4 (x \cdot x) - 3 \cdot x$

Multiply $x$ by $x$ .

$- 4 x^{2} - 3 \cdot x$

$- 4 x^{2} - 3 x$

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