Solve 3(5x-6)(3x+2)-6(3x+4)(x-1)-3(9x+1)(x-2)=0

$$3 ( 5 x - 6 ) ( 3 x + 2 ) - 6 ( 3 x + 4 ) ( x - 1 ) - 3 ( 9 x + 1 ) ( x - 2 ) = 0$$

Solve for x

$$x=\frac{2}{7}\approx 0.285714286$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 5x-6.

$$\left(15x-18\right)\left(3x+2\right)-6\left(3x+4\right)\left(x-1\right)-3\left(9x+1\right)\left(x-2\right)=0$$

Use the distributive property to multiply 15x-18 by 3x+2 and combine like terms.

$$45x^{2}-24x-36-6\left(3x+4\right)\left(x-1\right)-3\left(9x+1\right)\left(x-2\right)=0$$

Use the distributive property to multiply -6 by 3x+4.

$$45x^{2}-24x-36+\left(-18x-24\right)\left(x-1\right)-3\left(9x+1\right)\left(x-2\right)=0$$

Use the distributive property to multiply -18x-24 by x-1 and combine like terms.

$$45x^{2}-24x-36-18x^{2}-6x+24-3\left(9x+1\right)\left(x-2\right)=0$$

Combine 45x^{2} and -18x^{2} to get 27x^{2}.

$$27x^{2}-24x-36-6x+24-3\left(9x+1\right)\left(x-2\right)=0$$

Combine -24x and -6x to get -30x.

$$27x^{2}-30x-36+24-3\left(9x+1\right)\left(x-2\right)=0$$

Add -36 and 24 to get -12.

$$27x^{2}-30x-12-3\left(9x+1\right)\left(x-2\right)=0$$

Use the distributive property to multiply -3 by 9x+1.

$$27x^{2}-30x-12+\left(-27x-3\right)\left(x-2\right)=0$$

Use the distributive property to multiply -27x-3 by x-2 and combine like terms.

$$27x^{2}-30x-12-27x^{2}+51x+6=0$$

Combine 27x^{2} and -27x^{2} to get 0.

$$-30x-12+51x+6=0$$

Combine -30x and 51x to get 21x.

$$21x-12+6=0$$

Add -12 and 6 to get -6.

$$21x-6=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$21x=6$$

Divide both sides by 21.

$$x=\frac{6}{21}$$

Reduce the fraction \frac{6}{21} to lowest terms by extracting and canceling out 3.

$$x=\frac{2}{7}$$