Solve 3d^3=d^2(4b-5cx)

$$3 d ^ { 3 } = d ^ { 2 } ( 4 b - 5 c x )$$

Solve for b

$$\left\{\begin{matrix}\\b=\frac{5cx+3d}{4}\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply d^{2} by 4b-5cx.

$$3d^{3}=4d^{2}b-5d^{2}cx$$

Swap sides so that all variable terms are on the left hand side.

$$4d^{2}b-5d^{2}cx=3d^{3}$$

Add 5d^{2}cx to both sides.

$$4d^{2}b=3d^{3}+5d^{2}cx$$

The equation is in standard form.

$$4d^{2}b=5cxd^{2}+3d^{3}$$

Divide both sides by 4d^{2}.

$$\frac{4d^{2}b}{4d^{2}}=\frac{d^{2}\left(5cx+3d\right)}{4d^{2}}$$

Dividing by 4d^{2} undoes the multiplication by 4d^{2}.

$$b=\frac{d^{2}\left(5cx+3d\right)}{4d^{2}}$$

Divide \left(3d+5cx\right)d^{2} by 4d^{2}.

$$b=\frac{5cx+3d}{4}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{4b-3d}{5x}\text{, }&x\neq 0\\c\in \mathrm{R}\text{, }&d=0\text{ or }\left(d=\frac{4b}{3}\text{ and }x=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply d^{2} by 4b-5cx.

$$3d^{3}=4d^{2}b-5d^{2}cx$$

Swap sides so that all variable terms are on the left hand side.

$$4d^{2}b-5d^{2}cx=3d^{3}$$

Subtract 4d^{2}b from both sides.

$$-5d^{2}cx=3d^{3}-4d^{2}b$$

The equation is in standard form.

$$\left(-5xd^{2}\right)c=3d^{3}-4bd^{2}$$

Divide both sides by -5d^{2}x.

$$\frac{\left(-5xd^{2}\right)c}{-5xd^{2}}=\frac{\left(3d-4b\right)d^{2}}{-5xd^{2}}$$

Dividing by -5d^{2}x undoes the multiplication by -5d^{2}x.

$$c=\frac{\left(3d-4b\right)d^{2}}{-5xd^{2}}$$

Divide \left(3d-4b\right)d^{2} by -5d^{2}x.

$$c=-\frac{3d-4b}{5x}$$