Solve 3x^{3}+5x^3-7x^3+2x^3=3x^3

$$3 x ^ { 3 } + 5 x ^ { 3 } - 7 x ^ { 3 } + 2 x ^ { 3 } = 3 x ^ { 3 }$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Combine 3x^{3} and 5x^{3} to get 8x^{3}.

$$8x^{3}-7x^{3}+2x^{3}=3x^{3}$$

Combine 8x^{3} and -7x^{3} to get x^{3}.

$$x^{3}+2x^{3}=3x^{3}$$

Combine x^{3} and 2x^{3} to get 3x^{3}.

$$3x^{3}=3x^{3}$$

Subtract 3x^{3} from both sides.

$$3x^{3}-3x^{3}=0$$

Combine 3x^{3} and -3x^{3} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Combine 3x^{3} and 5x^{3} to get 8x^{3}.

$$8x^{3}-7x^{3}+2x^{3}=3x^{3}$$

Combine 8x^{3} and -7x^{3} to get x^{3}.

$$x^{3}+2x^{3}=3x^{3}$$

Combine x^{3} and 2x^{3} to get 3x^{3}.

$$3x^{3}=3x^{3}$$

Subtract 3x^{3} from both sides.

$$3x^{3}-3x^{3}=0$$

Combine 3x^{3} and -3x^{3} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$