Solve for t t(2t+3)+20=2t(t-3)

$t (2 t + 3) + 20 = 2 t (t - 3)$

Step 1

Simplify each term.

Apply the distributive property.

$t (2 t) + t \cdot 3 + 20 = 2 t (t - 3)$

Rewrite using the commutative property of multiplication.

$2 t \cdot t + t \cdot 3 + 20 = 2 t (t - 3)$

Move $3$ to the left of $t$ .

$2 t \cdot t + 3 \cdot t + 20 = 2 t (t - 3)$

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

Move $t$ .

$2 (t \cdot t) + 3 \cdot t + 20 = 2 t (t - 3)$

Multiply $t$ by $t$ .

$2 t^{2} + 3 \cdot t + 20 = 2 t (t - 3)$

$2 t^{2} + 3 t + 20 = 2 t (t - 3)$

Step 2

Simplify $2 t (t - 3)$ .

Apply the distributive property.

$2 t^{2} + 3 t + 20 = 2 t \cdot t + 2 t \cdot - 3$

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

Move $t$ .

$2 t^{2} + 3 t + 20 = 2 (t \cdot t) + 2 t \cdot - 3$

Multiply $t$ by $t$ .

$2 t^{2} + 3 t + 20 = 2 t^{2} + 2 t \cdot - 3$

Multiply $- 3$ by $2$ .

$2 t^{2} + 3 t + 20 = 2 t^{2} - 6 t$

Step 3

Move all terms containing $t$ to the left side of the equation.

Subtract $2 t^{2}$ from both sides of the equation.

$2 t^{2} + 3 t + 20 - 2 t^{2} = - 6 t$

Add $6 t$ to both sides of the equation.

$2 t^{2} + 3 t + 20 - 2 t^{2} + 6 t = 0$

Combine the opposite terms in $2 t^{2} + 3 t + 20 - 2 t^{2} + 6 t$ .

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

$3 t + 20 + 0 + 6 t = 0$

Add $3 t + 20$ and $0$ .

$3 t + 20 + 6 t = 0$

Add $3 t$ and $6 t$ .

$9 t + 20 = 0$

Step 4

Subtract $20$ from both sides of the equation.

$9 t = - 20$

Step 5

Divide each term in $9 t = - 20$ by $9$ and simplify.

Divide each term in $9 t = - 20$ by $9$ .

$\frac{9 t}{9} = \frac{- 20}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 t}{9} = \frac{- 20}{9}$

Divide $t$ by $1$ .

$t = \frac{- 20}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$t = - \frac{20}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{20}{9}$

Decimal Form:

$t = - 2.\overline{2}$

Mixed Number Form:

$t = - 2 \frac{2}{9}$

Solve for t t(2t+3)+20=2t(t-3)

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