Solve (2x-3)(x+7)=(x-4)(2x+3)+3

$$( 2 x - 3 ) ( x + 7 ) = ( x - 4 ) ( 2 x + 3 ) + 3$$

Solve for x

$$x=\frac{3}{4}=0.75$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-3 by x+7 and combine like terms.

$$2x^{2}+11x-21=\left(x-4\right)\left(2x+3\right)+3$$

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

$$2x^{2}+11x-21=2x^{2}-5x-12+3$$

Add -12 and 3 to get -9.

$$2x^{2}+11x-21=2x^{2}-5x-9$$

Subtract 2x^{2} from both sides.

$$2x^{2}+11x-21-2x^{2}=-5x-9$$

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

$$11x-21=-5x-9$$

Add 5x to both sides.

$$11x-21+5x=-9$$

Combine 11x and 5x to get 16x.

$$16x-21=-9$$

Add 21 to both sides.

$$16x=-9+21$$

Add -9 and 21 to get 12.

$$16x=12$$

Divide both sides by 16.

$$x=\frac{12}{16}$$

Reduce the fraction \frac{12}{16} to lowest terms by extracting and canceling out 4.

$$x=\frac{3}{4}$$