Solve x(x+4)-3=(x+1)(x-3)+6x

$$x ( x + 4 ) - 3 = ( x + 1 ) ( x - 3 ) + 6 x$$

Solve for x (complex solution)

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

Solution Steps

Use the distributive property to multiply x by x+4.

$$x^{2}+4x-3=\left(x+1\right)\left(x-3\right)+6x$$

Use the distributive property to multiply x+1 by x-3 and combine like terms.

$$x^{2}+4x-3=x^{2}-2x-3+6x$$

Combine -2x and 6x to get 4x.

$$x^{2}+4x-3=x^{2}+4x-3$$

Subtract x^{2} from both sides.

$$x^{2}+4x-3-x^{2}=4x-3$$

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

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

Subtract 4x from 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 by x+4.

$$x^{2}+4x-3=\left(x+1\right)\left(x-3\right)+6x$$

Use the distributive property to multiply x+1 by x-3 and combine like terms.

$$x^{2}+4x-3=x^{2}-2x-3+6x$$

Combine -2x and 6x to get 4x.

$$x^{2}+4x-3=x^{2}+4x-3$$

Subtract x^{2} from both sides.

$$x^{2}+4x-3-x^{2}=4x-3$$

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

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

Subtract 4x from 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.

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