Simplify (-30x^3y+12x^2y^2-18x^2y)÷(-6x^2y)

$(- 30 x^{3} y + 12 x^{2} y^{2} - 18 x^{2} y) \div (- 6 x^{2} y)$

Step 1

Rewrite the division as a fraction.

$\frac{- 30 x^{3} y + 12 x^{2} y^{2} - 18 x^{2} y}{- 6 x^{2} y}$

Step 2

Factor $6 x^{2} y$ out of $- 30 x^{3} y + 12 x^{2} y^{2} - 18 x^{2} y$ .

Factor $6 x^{2} y$ out of $- 30 x^{3} y$ .

$\frac{6 x^{2} y (- 5 x) + 12 x^{2} y^{2} - 18 x^{2} y}{- 6 x^{2} y}$

Factor $6 x^{2} y$ out of $12 x^{2} y^{2}$ .

$\frac{6 x^{2} y (- 5 x) + 6 x^{2} y (2 y) - 18 x^{2} y}{- 6 x^{2} y}$

Factor $6 x^{2} y$ out of $- 18 x^{2} y$ .

$\frac{6 x^{2} y (- 5 x) + 6 x^{2} y (2 y) + 6 x^{2} y (- 3)}{- 6 x^{2} y}$

Factor $6 x^{2} y$ out of $6 x^{2} y (- 5 x) + 6 x^{2} y (2 y)$ .

$\frac{6 x^{2} y (- 5 x + 2 y) + 6 x^{2} y (- 3)}{- 6 x^{2} y}$

Factor $6 x^{2} y$ out of $6 x^{2} y (- 5 x + 2 y) + 6 x^{2} y (- 3)$ .

$\frac{6 x^{2} y (- 5 x + 2 y - 3)}{- 6 x^{2} y}$

Step 3

Cancel the common factor of $6$ and $- 6$ .

Factor $6$ out of $6 x^{2} y (- 5 x + 2 y - 3)$ .

$\frac{6 (x^{2} y (- 5 x + 2 y - 3))}{- 6 x^{2} y}$

Cancel the common factors.

Factor $6$ out of $- 6 x^{2} y$ .

$\frac{6 (x^{2} y (- 5 x + 2 y - 3))}{6 (- x^{2} y)}$

Cancel the common factor.

$\frac{6 (x^{2} y (- 5 x + 2 y - 3))}{6 (- x^{2} y)}$

Rewrite the expression.

$\frac{x^{2} y (- 5 x + 2 y - 3)}{- x^{2} y}$

Step 4

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{x^{2} y (- 5 x + 2 y - 3)}{- x^{2} y}$

Rewrite the expression.

$\frac{y (- 5 x + 2 y - 3)}{- 1 y}$

Step 5

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{y (- 5 x + 2 y - 3)}{- 1 y}$

Rewrite the expression.

$\frac{- 5 x + 2 y - 3}{- 1}$

Move the negative one from the denominator of $\frac{- 5 x + 2 y - 3}{- 1}$ .

$- 1 \cdot (- 5 x + 2 y - 3)$

Step 6

Rewrite $- 1 \cdot (- 5 x + 2 y - 3)$ as $- (- 5 x + 2 y - 3)$ .

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

Step 7

Apply the distributive property.

$- (- 5 x) - (2 y) - - 3$

Step 8

Simplify.

Multiply $- 5$ by $- 1$ .

$5 x - (2 y) - - 3$

Multiply $2$ by $- 1$ .

$5 x - 2 y - - 3$

Multiply $- 1$ by $- 3$ .

$5 x - 2 y + 3$

Simplify (-30x^3y+12x^2y^2-18x^2y)÷(-6x^2y)

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