Solve (x+4)(3x-7)=(x-2)(3x+8)

$$( x + 4 ) ( 3 x - 7 ) = ( x - 2 ) ( 3 x + 8 )$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+4 by 3x-7 and combine like terms.

$$3x^{2}+5x-28=\left(x-2\right)\left(3x+8\right)$$

Use the distributive property to multiply x-2 by 3x+8 and combine like terms.

$$3x^{2}+5x-28=3x^{2}+2x-16$$

Subtract 3x^{2} from both sides.

$$3x^{2}+5x-28-3x^{2}=2x-16$$

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

$$5x-28=2x-16$$

Subtract 2x from both sides.

$$5x-28-2x=-16$$

Combine 5x and -2x to get 3x.

$$3x-28=-16$$

Add 28 to both sides.

$$3x=-16+28$$

Add -16 and 28 to get 12.

$$3x=12$$

Divide both sides by 3.

$$x=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$x=4$$