Simplify 6t(2t-3)-5(2t^2+9t-3)

$6 t (2 t - 3) - 5 (2 t^{2} + 9 t - 3)$

Step 1

Simplify each term.

Apply the distributive property.

$6 t (2 t) + 6 t \cdot - 3 - 5 (2 t^{2} + 9 t - 3)$

Rewrite using the commutative property of multiplication.

$6 \cdot 2 t \cdot t + 6 t \cdot - 3 - 5 (2 t^{2} + 9 t - 3)$

Multiply $- 3$ by $6$ .

$6 \cdot 2 t \cdot t - 18 t - 5 (2 t^{2} + 9 t - 3)$

Simplify each term.

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$6 \cdot 2 (t \cdot t) - 18 t - 5 (2 t^{2} + 9 t - 3)$

Multiply $t$ by $t$ .

$6 \cdot 2 t^{2} - 18 t - 5 (2 t^{2} + 9 t - 3)$

Multiply $6$ by $2$ .

$12 t^{2} - 18 t - 5 (2 t^{2} + 9 t - 3)$

Apply the distributive property.

$12 t^{2} - 18 t - 5 (2 t^{2}) - 5 (9 t) - 5 \cdot - 3$

Simplify.

Multiply $2$ by $- 5$ .

$12 t^{2} - 18 t - 10 t^{2} - 5 (9 t) - 5 \cdot - 3$

Multiply $9$ by $- 5$ .

$12 t^{2} - 18 t - 10 t^{2} - 45 t - 5 \cdot - 3$

Multiply $- 5$ by $- 3$ .

$12 t^{2} - 18 t - 10 t^{2} - 45 t + 15$

Step 2

Simplify by adding terms.

Subtract $10 t^{2}$ from $12 t^{2}$ .

$2 t^{2} - 18 t - 45 t + 15$

Subtract $45 t$ from $- 18 t$ .

$2 t^{2} - 63 t + 15$