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

$$\frac { 2 ( 5 x - 3 ) } { 3 } - \frac { 5 ( x - 6 ) } { 6 } = \frac { 3 ( 2 x + 1 ) } { 4 } - \frac { 4 ( 3 x ) } { 5 }$$

Solve for x

$$x=-\frac{45}{68}\approx -0.661764706$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 3,6,4,5.

$$20\times 2\left(5x-3\right)-10\times 5\left(x-6\right)=15\times 3\left(2x+1\right)-12\times 4\times 3x$$

Multiply 20 and 2 to get 40.

$$40\left(5x-3\right)-10\times 5\left(x-6\right)=15\times 3\left(2x+1\right)-12\times 4\times 3x$$

Use the distributive property to multiply 40 by 5x-3.

$$200x-120-10\times 5\left(x-6\right)=15\times 3\left(2x+1\right)-12\times 4\times 3x$$

Multiply -10 and 5 to get -50.

$$200x-120-50\left(x-6\right)=15\times 3\left(2x+1\right)-12\times 4\times 3x$$

Use the distributive property to multiply -50 by x-6.

$$200x-120-50x+300=15\times 3\left(2x+1\right)-12\times 4\times 3x$$

Combine 200x and -50x to get 150x.

$$150x-120+300=15\times 3\left(2x+1\right)-12\times 4\times 3x$$

Add -120 and 300 to get 180.

$$150x+180=15\times 3\left(2x+1\right)-12\times 4\times 3x$$

Multiply 15 and 3 to get 45. Multiply -12 and 4 to get -48.

$$150x+180=45\left(2x+1\right)-48\times 3x$$

Use the distributive property to multiply 45 by 2x+1.

$$150x+180=90x+45-48\times 3x$$

Multiply -48 and 3 to get -144.

$$150x+180=90x+45-144x$$

Combine 90x and -144x to get -54x.

$$150x+180=-54x+45$$

Add 54x to both sides.

$$150x+180+54x=45$$

Combine 150x and 54x to get 204x.

$$204x+180=45$$

Subtract 180 from both sides.

$$204x=45-180$$

Subtract 180 from 45 to get -135.

$$204x=-135$$

Divide both sides by 204.

$$x=\frac{-135}{204}$$

Reduce the fraction \frac{-135}{204} to lowest terms by extracting and canceling out 3.

$$x=-\frac{45}{68}$$