Simplify -2(3a^2+a-2b)+9(a+4b)+6a^2

$- 2 (3 a^{2} + a - 2 b) + 9 (a + 4 b) + 6 a^{2}$

Simplify each term.

Apply the distributive property.

$- 2 (3 a^{2}) - 2 a - 2 (- 2 b) + 9 (a + 4 b) + 6 a^{2}$

Simplify.

Multiply $3$ by $- 2$ .

$- 6 a^{2} - 2 a - 2 (- 2 b) + 9 (a + 4 b) + 6 a^{2}$

Multiply $- 2$ by $- 2$ .

$- 6 a^{2} - 2 a + 4 b + 9 (a + 4 b) + 6 a^{2}$

Apply the distributive property.

$- 6 a^{2} - 2 a + 4 b + 9 a + 9 (4 b) + 6 a^{2}$

Multiply $4$ by $9$ .

$- 6 a^{2} - 2 a + 4 b + 9 a + 36 b + 6 a^{2}$

Simplify by adding terms.

Combine the opposite terms in $- 6 a^{2} - 2 a + 4 b + 9 a + 36 b + 6 a^{2}$ .

Add $- 6 a^{2}$ and $6 a^{2}$ .

$- 2 a + 4 b + 9 a + 36 b + 0$

Add $- 2 a + 4 b + 9 a + 36 b$ and $0$ .

$- 2 a + 4 b + 9 a + 36 b$

Add $- 2 a$ and $9 a$ .

$7 a + 4 b + 36 b$

Add $4 b$ and $36 b$ .

$7 a + 40 b$