Solve (3x-2)(2x+7)-(3x+11)(2x-3)=0

$$( 3 x - 2 ) ( 2 x + 7 ) - ( 3 x + 11 ) ( 2 x - 3 ) = 0$$

Solve for x

$$x = -\frac{19}{4} = -4\frac{3}{4} = -4.75$$

Steps for Solving Linear Equation

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

$$6x^{2}+17x-14-\left(3x+11\right)\left(2x-3\right)=0$$

Use the distributive property to multiply 3x+11 by 2x-3 and combine like terms.

$$6x^{2}+17x-14-\left(6x^{2}+13x-33\right)=0$$

To find the opposite of 6x^{2}+13x-33, find the opposite of each term.

$$6x^{2}+17x-14-6x^{2}-13x+33=0$$

Combine 6x^{2} and -6x^{2} to get 0.

$$17x-14-13x+33=0$$

Combine 17x and -13x to get 4x.

$$4x-14+33=0$$

Add -14 and 33 to get 19.

$$4x+19=0$$

Subtract 19 from both sides. Anything subtracted from zero gives its negation.

$$4x=-19$$

Divide both sides by 4.

$$x=\frac{-19}{4}$$

Fraction \frac{-19}{4} can be rewritten as -\frac{19}{4} by extracting the negative sign.

$$x=-\frac{19}{4}$$