Solve x^3-4x+3=x^2(x-1)+x(x-1)-3(x-1)

$$x ^ { 3 } - 4 x + 3 = x ^ { 2 } ( x - 1 ) + x ( x - 1 ) - 3 ( x - 1 )$$

Solve for x (complex solution)

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

Solution Steps

Use the distributive property to multiply x^{2} by x-1.

$$x^{3}-4x+3=x^{3}-x^{2}+x\left(x-1\right)-3\left(x-1\right)$$

Use the distributive property to multiply x by x-1.

$$x^{3}-4x+3=x^{3}-x^{2}+x^{2}-x-3\left(x-1\right)$$

Combine -x^{2} and x^{2} to get 0.

$$x^{3}-4x+3=x^{3}-x-3\left(x-1\right)$$

Use the distributive property to multiply -3 by x-1.

$$x^{3}-4x+3=x^{3}-x-3x+3$$

Combine -x and -3x to get -4x.

$$x^{3}-4x+3=x^{3}-4x+3$$

Subtract x^{3} from both sides.

$$x^{3}-4x+3-x^{3}=-4x+3$$

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

$$-4x+3=-4x+3$$

Add 4x to both sides.

$$-4x+3+4x=3$$

Combine -4x and 4x to get 0.

$$3=3$$

Compare 3 and 3.

$$\text{true}$$

This is true for any x.

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

Solve for x

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

Solution Steps

Use the distributive property to multiply x^{2} by x-1.

$$x^{3}-4x+3=x^{3}-x^{2}+x\left(x-1\right)-3\left(x-1\right)$$

Use the distributive property to multiply x by x-1.

$$x^{3}-4x+3=x^{3}-x^{2}+x^{2}-x-3\left(x-1\right)$$

Combine -x^{2} and x^{2} to get 0.

$$x^{3}-4x+3=x^{3}-x-3\left(x-1\right)$$

Use the distributive property to multiply -3 by x-1.

$$x^{3}-4x+3=x^{3}-x-3x+3$$

Combine -x and -3x to get -4x.

$$x^{3}-4x+3=x^{3}-4x+3$$

Subtract x^{3} from both sides.

$$x^{3}-4x+3-x^{3}=-4x+3$$

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

$$-4x+3=-4x+3$$

Add 4x to both sides.

$$-4x+3+4x=3$$

Combine -4x and 4x to get 0.

$$3=3$$

Compare 3 and 3.

$$\text{true}$$

This is true for any x.

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