Solve dh=(15t+6)dt

$$d h = ( 15 t + 6 ) d t$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&h=3t\left(5t+2\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 15t+6 by d.

$$dh=\left(15td+6d\right)t$$

Use the distributive property to multiply 15td+6d by t.

$$dh=15dt^{2}+6dt$$

Subtract 15dt^{2} from both sides.

$$dh-15dt^{2}=6dt$$

Subtract 6dt from both sides.

$$dh-15dt^{2}-6dt=0$$

Combine all terms containing d.

$$\left(h-15t^{2}-6t\right)d=0$$

The equation is in standard form.

$$\left(h-6t-15t^{2}\right)d=0$$

Divide 0 by -15t^{2}-6t+h.

$$d=0$$

Solve for h

$$\left\{\begin{matrix}\\h=3t\left(5t+2\right)\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 15t+6 by d.

$$dh=\left(15td+6d\right)t$$

Use the distributive property to multiply 15td+6d by t.

$$dh=15dt^{2}+6dt$$

Divide both sides by d.

$$\frac{dh}{d}=\frac{3dt\left(5t+2\right)}{d}$$

Dividing by d undoes the multiplication by d.

$$h=\frac{3dt\left(5t+2\right)}{d}$$

Divide 3dt\left(2+5t\right) by d.

$$h=3t\left(5t+2\right)$$