Solve 3(x-1)(x+2)=3(x^2+x-2)=3x^2+3x-6

$$3 ( x - 1 ) ( x + 2 ) = 3 ( x ^ { 2 } + x - 2 ) = 3 x ^ { 2 } + 3 x - 6$$

Evaluate (complex solution)

Solution Steps

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

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

Use the distributive property to multiply 3x-3 by x+2 and combine like terms.

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

Use the distributive property to multiply 3 by x^{2}+x-2.

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

Use the distributive property to multiply 3 by x^{2}+x-2.

$$3x^{2}+3x-6=3x^{2}+3x-6\text{ and }3x^{2}+3x-6=3x^{2}+3x-6$$

Subtract 3x^{2} from both sides.

$$3x^{2}+3x-6-3x^{2}=3x-6\text{ and }3x^{2}+3x-6=3x^{2}+3x-6$$

Combine 3x^{2} and -3x^{2} to get 0.

$$3x-6=3x-6\text{ and }3x^{2}+3x-6=3x^{2}+3x-6$$

Subtract 3x from both sides.

$$3x-6-3x=-6\text{ and }3x^{2}+3x-6=3x^{2}+3x-6$$

Combine 3x and -3x to get 0.

$$-6=-6\text{ and }3x^{2}+3x-6=3x^{2}+3x-6$$

Compare -6 and -6.

$$\text{true}\text{ and }3x^{2}+3x-6=3x^{2}+3x-6$$

Subtract 3x^{2} from both sides.

$$\text{true}\text{ and }3x^{2}+3x-6-3x^{2}=3x-6$$

Combine 3x^{2} and -3x^{2} to get 0.

$$\text{true}\text{ and }3x-6=3x-6$$

Subtract 3x from both sides.

$$\text{true}\text{ and }3x-6-3x=-6$$

Combine 3x and -3x to get 0.

$$\text{true}\text{ and }-6=-6$$

Compare -6 and -6.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$

Solve for x

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