Solve 32m^4+12m^3=4m^3(8m+3)

$$32 m ^ { 4 } + 12 m ^ { 3 } = 4 m ^ { 3 } ( 8 m + 3 )$$

Solve for m (complex solution)

$$m\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply 4m^{3} by 8m+3.

$$32m^{4}+12m^{3}=32m^{4}+12m^{3}$$

Subtract 32m^{4} from both sides.

$$32m^{4}+12m^{3}-32m^{4}=12m^{3}$$

Combine 32m^{4} and -32m^{4} to get 0.

$$12m^{3}=12m^{3}$$

Subtract 12m^{3} from both sides.

$$12m^{3}-12m^{3}=0$$

Combine 12m^{3} and -12m^{3} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any m.

$$m\in \mathrm{C}$$

Solve for m

$$m\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 4m^{3} by 8m+3.

$$32m^{4}+12m^{3}=32m^{4}+12m^{3}$$

Subtract 32m^{4} from both sides.

$$32m^{4}+12m^{3}-32m^{4}=12m^{3}$$

Combine 32m^{4} and -32m^{4} to get 0.

$$12m^{3}=12m^{3}$$

Subtract 12m^{3} from both sides.

$$12m^{3}-12m^{3}=0$$

Combine 12m^{3} and -12m^{3} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any m.

$$m\in \mathrm{R}$$