Solve 40w^3p-24wp^2=8wp(5w^2-3p)

$$40 w ^ { 3 } p - 24 w p ^ { 2 } = 8 w p ( 5 w ^ { 2 } - 3 p )$$

Solve for p (complex solution)

$$p\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply 8wp by 5w^{2}-3p.

$$40w^{3}p-24wp^{2}=40w^{3}p-24wp^{2}$$

Subtract 40w^{3}p from both sides.

$$40w^{3}p-24wp^{2}-40w^{3}p=-24wp^{2}$$

Add 24wp^{2} to both sides.

$$40w^{3}p-24wp^{2}-40w^{3}p+24wp^{2}=0$$

Combine 40w^{3}p and -40w^{3}p to get 0.

$$-24wp^{2}+24wp^{2}=0$$

Combine -24wp^{2} and 24wp^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any p.

$$p\in \mathrm{C}$$

Solve for w (complex solution)

$$w\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply 8wp by 5w^{2}-3p.

$$40w^{3}p-24wp^{2}=40w^{3}p-24wp^{2}$$

Subtract 40w^{3}p from both sides.

$$40w^{3}p-24wp^{2}-40w^{3}p=-24wp^{2}$$

Add 24wp^{2} to both sides.

$$40w^{3}p-24wp^{2}-40w^{3}p+24wp^{2}=0$$

Combine 40w^{3}p and -40w^{3}p to get 0.

$$-24wp^{2}+24wp^{2}=0$$

Combine -24wp^{2} and 24wp^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any w.

$$w\in \mathrm{C}$$

Solve for p

$$p\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 8wp by 5w^{2}-3p.

$$40w^{3}p-24wp^{2}=40w^{3}p-24wp^{2}$$

Subtract 40w^{3}p from both sides.

$$40w^{3}p-24wp^{2}-40w^{3}p=-24wp^{2}$$

Add 24wp^{2} to both sides.

$$40w^{3}p-24wp^{2}-40w^{3}p+24wp^{2}=0$$

Combine 40w^{3}p and -40w^{3}p to get 0.

$$-24wp^{2}+24wp^{2}=0$$

Combine -24wp^{2} and 24wp^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any p.

$$p\in \mathrm{R}$$

Solve for w

$$w\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 8wp by 5w^{2}-3p.

$$40w^{3}p-24wp^{2}=40w^{3}p-24wp^{2}$$

Subtract 40w^{3}p from both sides.

$$40w^{3}p-24wp^{2}-40w^{3}p=-24wp^{2}$$

Add 24wp^{2} to both sides.

$$40w^{3}p-24wp^{2}-40w^{3}p+24wp^{2}=0$$

Combine 40w^{3}p and -40w^{3}p to get 0.

$$-24wp^{2}+24wp^{2}=0$$

Combine -24wp^{2} and 24wp^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any w.

$$w\in \mathrm{R}$$