Solve s=4tleft(s+3right)/2t+2

$$s = \frac{ 4t \left( s+3 \right) }{ 2t+2 }$$

Solve for s

$$s=\frac{6t}{1-t}$$

$$|t|\neq 1$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{4t\left(s+3\right)}{2t+2}.

$$s=\frac{4t\left(s+3\right)}{2\left(t+1\right)}$$

Cancel out 2 in both numerator and denominator.

$$s=\frac{2t\left(s+3\right)}{t+1}$$

Use the distributive property to multiply 2t by s+3.

$$s=\frac{2ts+6t}{t+1}$$

Subtract \frac{2ts+6t}{t+1} from both sides.

$$s-\frac{2ts+6t}{t+1}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply s times \frac{t+1}{t+1}.

$$\frac{s\left(t+1\right)}{t+1}-\frac{2ts+6t}{t+1}=0$$

Since \frac{s\left(t+1\right)}{t+1} and \frac{2ts+6t}{t+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{s\left(t+1\right)-\left(2ts+6t\right)}{t+1}=0$$

Do the multiplications in s\left(t+1\right)-\left(2ts+6t\right).

$$\frac{st+s-2ts-6t}{t+1}=0$$

Combine like terms in st+s-2ts-6t.

$$\frac{-st+s-6t}{t+1}=0$$

Multiply both sides of the equation by t+1.

$$-st+s-6t=0$$

Add 6t to both sides. Anything plus zero gives itself.

$$-st+s=6t$$

Combine all terms containing s.

$$\left(-t+1\right)s=6t$$

The equation is in standard form.

$$\left(1-t\right)s=6t$$

Divide both sides by -t+1.

$$\frac{\left(1-t\right)s}{1-t}=\frac{6t}{1-t}$$

Dividing by -t+1 undoes the multiplication by -t+1.

$$s=\frac{6t}{1-t}$$

Solve for t

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

$$s\neq -3\text{ and }s\neq -6$$

Steps for Solving Linear Equation

Variable t cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by 2\left(t+1\right).

$$s\times 2\left(t+1\right)=4t\left(s+3\right)$$

Use the distributive property to multiply s\times 2 by t+1.

$$2st+s\times 2=4t\left(s+3\right)$$

Use the distributive property to multiply 4t by s+3.

$$2st+s\times 2=4ts+12t$$

Subtract 4ts from both sides.

$$2st+s\times 2-4ts=12t$$

Combine 2st and -4ts to get -2st.

$$-2st+s\times 2=12t$$

Subtract 12t from both sides.

$$-2st+s\times 2-12t=0$$

Subtract s\times 2 from both sides. Anything subtracted from zero gives its negation.

$$-2st-12t=-s\times 2$$

Multiply -1 and 2 to get -2.

$$-2st-12t=-2s$$

Combine all terms containing t.

$$\left(-2s-12\right)t=-2s$$

Divide both sides by -2s-12.

$$\frac{\left(-2s-12\right)t}{-2s-12}=-\frac{2s}{-2s-12}$$

Dividing by -2s-12 undoes the multiplication by -2s-12.

$$t=-\frac{2s}{-2s-12}$$

Divide -2s by -2s-12.

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

Variable t cannot be equal to -1.

$$t=\frac{s}{s+6}\text{, }t\neq -1$$