Solve 2(x+1)(3x+2)-(x-1)(x-2)=5(x+1)(x-1)

$$2(x+1)(3x+2)-(x-1)(x-2)=5(x+1)(x-1)$$

Solve for x

$$x=-\frac{7}{13}\approx -0.538461538$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x+1.

$$\left(2x+2\right)\left(3x+2\right)-\left(x-1\right)\left(x-2\right)=5\left(x+1\right)\left(x-1\right)$$

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

$$6x^{2}+10x+4-\left(x-1\right)\left(x-2\right)=5\left(x+1\right)\left(x-1\right)$$

Use the distributive property to multiply x-1 by x-2 and combine like terms.

$$6x^{2}+10x+4-\left(x^{2}-3x+2\right)=5\left(x+1\right)\left(x-1\right)$$

To find the opposite of x^{2}-3x+2, find the opposite of each term.

$$6x^{2}+10x+4-x^{2}+3x-2=5\left(x+1\right)\left(x-1\right)$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}+10x+4+3x-2=5\left(x+1\right)\left(x-1\right)$$

Combine 10x and 3x to get 13x.

$$5x^{2}+13x+4-2=5\left(x+1\right)\left(x-1\right)$$

Subtract 2 from 4 to get 2.

$$5x^{2}+13x+2=5\left(x+1\right)\left(x-1\right)$$

Use the distributive property to multiply 5 by x+1.

$$5x^{2}+13x+2=\left(5x+5\right)\left(x-1\right)$$

Use the distributive property to multiply 5x+5 by x-1 and combine like terms.

$$5x^{2}+13x+2=5x^{2}-5$$

Subtract 5x^{2} from both sides.

$$5x^{2}+13x+2-5x^{2}=-5$$

Combine 5x^{2} and -5x^{2} to get 0.

$$13x+2=-5$$

Subtract 2 from both sides.

$$13x=-5-2$$

Subtract 2 from -5 to get -7.

$$13x=-7$$

Divide both sides by 13.

$$x=\frac{-7}{13}$$

Fraction \frac{-7}{13} can be rewritten as -\frac{7}{13} by extracting the negative sign.

$$x=-\frac{7}{13}$$