Solve (3x-2)(4x+1)/6x(x+3-2=0

$$\frac { ( 3 x - 2 ) ( 4 x + 1 ) } { 6 x ( x + 3 } - 2 = 0$$

Solve for x

$$x=-\frac{2}{41}\approx -0.048780488$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,0 since division by zero is not defined. Multiply both sides of the equation by 6x\left(x+3\right).

$$\left(3x-2\right)\left(4x+1\right)+6x\left(x+3\right)\left(-2\right)=0$$

Use the distributive property to multiply 3x-2 by 4x+1 and combine like terms.

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

Multiply 6 and -2 to get -12.

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

Use the distributive property to multiply -12x by x+3.

$$12x^{2}-5x-2-12x^{2}-36x=0$$

Combine 12x^{2} and -12x^{2} to get 0.

$$-5x-2-36x=0$$

Combine -5x and -36x to get -41x.

$$-41x-2=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$-41x=2$$

Divide both sides by -41.

$$x=\frac{2}{-41}$$

Fraction \frac{2}{-41} can be rewritten as -\frac{2}{41} by extracting the negative sign.

$$x=-\frac{2}{41}$$