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

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

Solve for x

$$x = -\frac{67}{61} = -1\frac{6}{61} \approx -1.098360656$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3\times 4\left(3x+6\right)+45=5\times 2\left(2x+5\right)-45x$$

Multiply 3 and 4 to get 12.

$$12\left(3x+6\right)+45=5\times 2\left(2x+5\right)-45x$$

Use the distributive property to multiply 12 by 3x+6.

$$36x+72+45=5\times 2\left(2x+5\right)-45x$$

Add 72 and 45 to get 117.

$$36x+117=5\times 2\left(2x+5\right)-45x$$

Multiply 5 and 2 to get 10.

$$36x+117=10\left(2x+5\right)-45x$$

Use the distributive property to multiply 10 by 2x+5.

$$36x+117=20x+50-45x$$

Combine 20x and -45x to get -25x.

$$36x+117=-25x+50$$

Add 25x to both sides.

$$36x+117+25x=50$$

Combine 36x and 25x to get 61x.

$$61x+117=50$$

Subtract 117 from both sides.

$$61x=50-117$$

Subtract 117 from 50 to get -67.

$$61x=-67$$

Divide both sides by 61.

$$x=\frac{-67}{61}$$

Fraction \frac{-67}{61} can be rewritten as -\frac{67}{61} by extracting the negative sign.

$$x=-\frac{67}{61}$$