Solve 3(x+1)(x-1)-3(x-1)^2+2=18

$$3 ( x + 1 ) ( x - 1 ) - 3 ( x - 1 ) ^ { 2 } + 2 = 18$$

Solve for x

$$x = \frac{11}{3} = 3\frac{2}{3} \approx 3.666666667$$

Steps for Solving Linear Equation

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

$$\left(3x+3\right)\left(x-1\right)-3\left(x-1\right)^{2}+2=18$$

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

$$3x^{2}-3-3\left(x-1\right)^{2}+2=18$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$3x^{2}-3-3\left(x^{2}-2x+1\right)+2=18$$

Use the distributive property to multiply -3 by x^{2}-2x+1.

$$3x^{2}-3-3x^{2}+6x-3+2=18$$

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

$$-3+6x-3+2=18$$

Subtract 3 from -3 to get -6.

$$-6+6x+2=18$$

Add -6 and 2 to get -4.

$$-4+6x=18$$

Add 4 to both sides.

$$6x=18+4$$

Add 18 and 4 to get 22.

$$6x=22$$

Divide both sides by 6.

$$x=\frac{22}{6}$$

Reduce the fraction \frac{22}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{11}{3}$$