Solve 2(3y-2)=8(2y-3)(v)

$$2 ( 3 y - 2 ) = 8 ( 2 y - 3 ) ( v )$$

Solve for v

$$v=-\frac{3y-2}{4\left(3-2y\right)}$$

$$y\neq \frac{3}{2}$$

Steps for Solving Linear Equation

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

$$6y-4=8\left(2y-3\right)v$$

Use the distributive property to multiply 8 by 2y-3.

$$6y-4=\left(16y-24\right)v$$

Use the distributive property to multiply 16y-24 by v.

$$6y-4=16yv-24v$$

Swap sides so that all variable terms are on the left hand side.

$$16yv-24v=6y-4$$

Combine all terms containing v.

$$\left(16y-24\right)v=6y-4$$

Divide both sides by 16y-24.

$$\frac{\left(16y-24\right)v}{16y-24}=\frac{6y-4}{16y-24}$$

Dividing by 16y-24 undoes the multiplication by 16y-24.

$$v=\frac{6y-4}{16y-24}$$

Divide 6y-4 by 16y-24.

$$v=\frac{3y-2}{4\left(2y-3\right)}$$

Solve for y

$$y=-\frac{2\left(6v-1\right)}{3-8v}$$

$$v\neq \frac{3}{8}$$

Steps for Solving Linear Equation

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

$$6y-4=8\left(2y-3\right)v$$

Use the distributive property to multiply 8 by 2y-3.

$$6y-4=\left(16y-24\right)v$$

Use the distributive property to multiply 16y-24 by v.

$$6y-4=16yv-24v$$

Subtract 16yv from both sides.

$$6y-4-16yv=-24v$$

Add 4 to both sides.

$$6y-16yv=-24v+4$$

Combine all terms containing y.

$$\left(6-16v\right)y=-24v+4$$

The equation is in standard form.

$$\left(6-16v\right)y=4-24v$$

Divide both sides by -16v+6.

$$\frac{\left(6-16v\right)y}{6-16v}=\frac{4-24v}{6-16v}$$

Dividing by -16v+6 undoes the multiplication by -16v+6.

$$y=\frac{4-24v}{6-16v}$$

Divide -24v+4 by -16v+6.

$$y=\frac{2\left(1-6v\right)}{3-8v}$$