Solve (-2-y-3z/2)-2y+3(8-3y/-5)=-12

$$( \frac { - 2 - y - 3 z } { 2 } ) - 2 y + 3 ( \frac { 8 - 3 y } { - 5 } ) = - 12$$

Solve for y

$$y=\frac{62-15z}{7}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,-5.

$$5\left(-2-y-3z\right)-20y-6\left(8-3y\right)=-120$$

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

$$-10-5y-15z-20y-6\left(8-3y\right)=-120$$

Combine -5y and -20y to get -25y.

$$-10-25y-15z-6\left(8-3y\right)=-120$$

Use the distributive property to multiply -6 by 8-3y.

$$-10-25y-15z-48+18y=-120$$

Subtract 48 from -10 to get -58.

$$-58-25y-15z+18y=-120$$

Combine -25y and 18y to get -7y.

$$-58-7y-15z=-120$$

Add 58 to both sides.

$$-7y-15z=-120+58$$

Add -120 and 58 to get -62.

$$-7y-15z=-62$$

Add 15z to both sides.

$$-7y=-62+15z$$

The equation is in standard form.

$$-7y=15z-62$$

Divide both sides by -7.

$$\frac{-7y}{-7}=\frac{15z-62}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$y=\frac{15z-62}{-7}$$

Divide -62+15z by -7.

$$y=\frac{62-15z}{7}$$

Solve for z

$$z=\frac{62-7y}{15}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,-5.

$$5\left(-2-y-3z\right)-20y-6\left(8-3y\right)=-120$$

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

$$-10-5y-15z-20y-6\left(8-3y\right)=-120$$

Combine -5y and -20y to get -25y.

$$-10-25y-15z-6\left(8-3y\right)=-120$$

Use the distributive property to multiply -6 by 8-3y.

$$-10-25y-15z-48+18y=-120$$

Subtract 48 from -10 to get -58.

$$-58-25y-15z+18y=-120$$

Combine -25y and 18y to get -7y.

$$-58-7y-15z=-120$$

Add 58 to both sides.

$$-7y-15z=-120+58$$

Add -120 and 58 to get -62.

$$-7y-15z=-62$$

Add 7y to both sides.

$$-15z=-62+7y$$

The equation is in standard form.

$$-15z=7y-62$$

Divide both sides by -15.

$$\frac{-15z}{-15}=\frac{7y-62}{-15}$$

Dividing by -15 undoes the multiplication by -15.

$$z=\frac{7y-62}{-15}$$

Divide -62+7y by -15.

$$z=\frac{62-7y}{15}$$