Solve (2x-4)(3x+5)-(5x-5)(x-1)=(x-2)(x+3)-13

$$( 2 x - 4 ) ( 3 x + 5 ) - ( 5 x - 5 ) ( x - 1 ) = ( x - 2 ) ( x + 3 ) - 13$$

Solve for x

$$x=\frac{6}{7}\approx 0.857142857$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-4 by 3x+5 and combine like terms.

$$6x^{2}-2x-20-\left(5x-5\right)\left(x-1\right)=\left(x-2\right)\left(x+3\right)-13$$

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

$$6x^{2}-2x-20-\left(5x^{2}-10x+5\right)=\left(x-2\right)\left(x+3\right)-13$$

To find the opposite of 5x^{2}-10x+5, find the opposite of each term.

$$6x^{2}-2x-20-5x^{2}+10x-5=\left(x-2\right)\left(x+3\right)-13$$

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

$$x^{2}-2x-20+10x-5=\left(x-2\right)\left(x+3\right)-13$$

Combine -2x and 10x to get 8x.

$$x^{2}+8x-20-5=\left(x-2\right)\left(x+3\right)-13$$

Subtract 5 from -20 to get -25.

$$x^{2}+8x-25=\left(x-2\right)\left(x+3\right)-13$$

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

$$x^{2}+8x-25=x^{2}+x-6-13$$

Subtract 13 from -6 to get -19.

$$x^{2}+8x-25=x^{2}+x-19$$

Subtract x^{2} from both sides.

$$x^{2}+8x-25-x^{2}=x-19$$

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

$$8x-25=x-19$$

Subtract x from both sides.

$$8x-25-x=-19$$

Combine 8x and -x to get 7x.

$$7x-25=-19$$

Add 25 to both sides.

$$7x=-19+25$$

Add -19 and 25 to get 6.

$$7x=6$$

Divide both sides by 7.

$$x=\frac{6}{7}$$