Solve (5x-1)(x+2)-(x+1)(2x+3)=(3x+1)(x+2)-7

$$( 5 x - 1 ) ( x + 2 ) - ( x + 1 ) ( 2 x + 3 ) = ( 3 x + 1 ) ( x + 2 ) - 7$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5x-1 by x+2 and combine like terms.

$$5x^{2}+9x-2-\left(x+1\right)\left(2x+3\right)=\left(3x+1\right)\left(x+2\right)-7$$

Use the distributive property to multiply x+1 by 2x+3 and combine like terms.

$$5x^{2}+9x-2-\left(2x^{2}+5x+3\right)=\left(3x+1\right)\left(x+2\right)-7$$

To find the opposite of 2x^{2}+5x+3, find the opposite of each term.

$$5x^{2}+9x-2-2x^{2}-5x-3=\left(3x+1\right)\left(x+2\right)-7$$

Combine 5x^{2} and -2x^{2} to get 3x^{2}.

$$3x^{2}+9x-2-5x-3=\left(3x+1\right)\left(x+2\right)-7$$

Combine 9x and -5x to get 4x.

$$3x^{2}+4x-2-3=\left(3x+1\right)\left(x+2\right)-7$$

Subtract 3 from -2 to get -5.

$$3x^{2}+4x-5=\left(3x+1\right)\left(x+2\right)-7$$

Use the distributive property to multiply 3x+1 by x+2 and combine like terms.

$$3x^{2}+4x-5=3x^{2}+7x+2-7$$

Subtract 7 from 2 to get -5.

$$3x^{2}+4x-5=3x^{2}+7x-5$$

Subtract 3x^{2} from both sides.

$$3x^{2}+4x-5-3x^{2}=7x-5$$

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

$$4x-5=7x-5$$

Subtract 7x from both sides.

$$4x-5-7x=-5$$

Combine 4x and -7x to get -3x.

$$-3x-5=-5$$

Add 5 to both sides.

$$-3x=-5+5$$

Add -5 and 5 to get 0.

$$-3x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -3 is not equal to 0, x must be equal to 0.

$$x=0$$