Solve (3x-4)(2x+3)-(2x-5)(3x-1)=0

$$( 3 x - 4 ) ( 2 x + 3 ) - ( 2 x - 5 ) ( 3 x - 1 ) = 0$$

Solve for x

$$x=\frac{17}{18}\approx 0.944444444$$

Steps for Solving Linear Equation

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

$$6x^{2}+x-12-\left(2x-5\right)\left(3x-1\right)=0$$

Use the distributive property to multiply 2x-5 by 3x-1 and combine like terms.

$$6x^{2}+x-12-\left(6x^{2}-17x+5\right)=0$$

To find the opposite of 6x^{2}-17x+5, find the opposite of each term.

$$6x^{2}+x-12-6x^{2}+17x-5=0$$

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

$$x-12+17x-5=0$$

Combine x and 17x to get 18x.

$$18x-12-5=0$$

Subtract 5 from -12 to get -17.

$$18x-17=0$$

Add 17 to both sides. Anything plus zero gives itself.

$$18x=17$$

Divide both sides by 18.

$$x=\frac{17}{18}$$