Solve dh=(1.5t+6)dt

$$d h = ( 1.5 t + 6 ) d t$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&h=t\left(\frac{3t}{2}+6\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1.5t+6 by d.

$$dh=\left(1.5td+6d\right)t$$

Use the distributive property to multiply 1.5td+6d by t.

$$dh=1.5dt^{2}+6dt$$

Subtract 1.5dt^{2} from both sides.

$$dh-1.5dt^{2}=6dt$$

Subtract 6dt from both sides.

$$dh-1.5dt^{2}-6dt=0$$

Combine all terms containing d.

$$\left(h-1.5t^{2}-6t\right)d=0$$

The equation is in standard form.

$$\left(-\frac{3t^{2}}{2}+h-6t\right)d=0$$

Divide 0 by -1.5t^{2}-6t+h.

$$d=0$$

Solve for h

$$\left\{\begin{matrix}\\h=t\left(\frac{3t}{2}+6\right)\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1.5t+6 by d.

$$dh=\left(1.5td+6d\right)t$$

Use the distributive property to multiply 1.5td+6d by t.

$$dh=1.5dt^{2}+6dt$$

The equation is in standard form.

$$dh=\frac{3dt^{2}}{2}+6dt$$

Divide both sides by d.

$$\frac{dh}{d}=\frac{dt\left(\frac{3t}{2}+6\right)}{d}$$

Dividing by d undoes the multiplication by d.

$$h=\frac{dt\left(\frac{3t}{2}+6\right)}{d}$$

Divide dt\left(6+\frac{3t}{2}\right) by d.

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