Solve 3*{2+5*[x+4*(x/2-3)]*3}*9+6=30

$$3 \cdot \{ 2 + 5 \cdot [ x + 4 \cdot ( \frac { x } { 2 } - 3 ) ] \cdot 3 \} \cdot 9 + 6 = 30$$

Solve for x

$$x = \frac{322}{81} = 3\frac{79}{81} \approx 3.975308642$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$6\left(2+5\left(x+4\left(\frac{x}{2}-3\right)\right)\times 3\right)\times 9+12=60$$

Use the distributive property to multiply 4 by \frac{x}{2}-3.

$$6\left(2+5\left(x+4\times \frac{x}{2}-12\right)\times 3\right)\times 9+12=60$$

Cancel out 2, the greatest common factor in 4 and 2.

$$6\left(2+5\left(x+2x-12\right)\times 3\right)\times 9+12=60$$

Combine x and 2x to get 3x.

$$6\left(2+5\left(3x-12\right)\times 3\right)\times 9+12=60$$

Multiply 5 and 3 to get 15.

$$6\left(2+15\left(3x-12\right)\right)\times 9+12=60$$

Use the distributive property to multiply 15 by 3x-12.

$$6\left(2+45x-180\right)\times 9+12=60$$

Subtract 180 from 2 to get -178.

$$6\left(-178+45x\right)\times 9+12=60$$

Multiply 6 and 9 to get 54.

$$54\left(-178+45x\right)+12=60$$

Use the distributive property to multiply 54 by -178+45x.

$$-9612+2430x+12=60$$

Add -9612 and 12 to get -9600.

$$-9600+2430x=60$$

Add 9600 to both sides.

$$2430x=60+9600$$

Add 60 and 9600 to get 9660.

$$2430x=9660$$

Divide both sides by 2430.

$$x=\frac{9660}{2430}$$

Reduce the fraction \frac{9660}{2430} to lowest terms by extracting and canceling out 30.

$$x=\frac{322}{81}$$