Solve for t S(t)=2t3/2-9t+6

$S (t) = 2 t \frac{3}{2} - 9 t + 6$

Step 1

Since $t$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 t (\frac{3}{2}) - 9 t + 6 = S t$

Step 2

Simplify $2 t (\frac{3}{2}) - 9 t + 6$ .

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $2 t$ .

$2 (t) \frac{3}{2} - 9 t + 6 = S t$

Cancel the common factor.

$2 t \frac{3}{2} - 9 t + 6 = S t$

Rewrite the expression.

$t \cdot 3 - 9 t + 6 = S t$

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

$3 t - 9 t + 6 = S t$

Subtract $9 t$ from $3 t$ .

$- 6 t + 6 = S t$

Step 3

Subtract $S t$ from both sides of the equation.

$- 6 t + 6 - S t = 0$

Step 4

Subtract $6$ from both sides of the equation.

$- 6 t - S t = - 6$

Step 5

Factor $t$ out of $- 6 t - S t$ .

Factor $t$ out of $- 6 t$ .

$t \cdot - 6 - S t = - 6$

Factor $t$ out of $- S t$ .

$t \cdot - 6 + t (- S) = - 6$

Factor $t$ out of $t \cdot - 6 + t (- S)$ .

$t (- 6 - S) = - 6$

Step 6

Divide each term in $t (- 6 - S) = - 6$ by $- 6 - S$ and simplify.

Divide each term in $t (- 6 - S) = - 6$ by $- 6 - S$ .

$\frac{t (- 6 - S)}{- 6 - S} = \frac{- 6}{- 6 - S}$

Simplify the left side.

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

Cancel the common factor.

$\frac{t (- 6 - S)}{- 6 - S} = \frac{- 6}{- 6 - S}$

Divide $t$ by $1$ .

$t = \frac{- 6}{- 6 - S}$

Simplify the right side.

Move the negative in front of the fraction.

$t = - \frac{6}{- 6 - S}$

Rewrite $- 6$ as $- 1 (6)$ .

$t = - \frac{6}{- 1 (6) - S}$

Factor $- 1$ out of $- S$ .

$t = - \frac{6}{- 1 (6) - (S)}$

Factor $- 1$ out of $- 1 (6) - (S)$ .

$t = - \frac{6}{- 1 (6 + S)}$

Simplify the expression.

Move the negative in front of the fraction.

$t = - - \frac{6}{6 + S}$

Multiply $- 1$ by $- 1$ .

$t = 1 \frac{6}{6 + S}$

Multiply $\frac{6}{6 + S}$ by $1$ .

$t = \frac{6}{6 + S}$

Solve for t S(t)=2t3/2-9t+6

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