Solve 5/y+6=2/3-2y

$$\frac { 5 } { y + 6 } = \frac { 2 } { 3 - 2 y }$$

Solve for y

$$y=\frac{1}{4}=0.25$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -6,\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2y-3\right)\left(y+6\right), the least common multiple of y+6,3-2y.

$$\left(2y-3\right)\times 5=-\left(6+y\right)\times 2$$

Use the distributive property to multiply 2y-3 by 5.

$$10y-15=-\left(6+y\right)\times 2$$

Multiply -1 and 2 to get -2.

$$10y-15=-2\left(6+y\right)$$

Use the distributive property to multiply -2 by 6+y.

$$10y-15=-12-2y$$

Add 2y to both sides.

$$10y-15+2y=-12$$

Combine 10y and 2y to get 12y.

$$12y-15=-12$$

Add 15 to both sides.

$$12y=-12+15$$

Add -12 and 15 to get 3.

$$12y=3$$

Divide both sides by 12.

$$y=\frac{3}{12}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$y=\frac{1}{4}$$