Solve frac{V_{3}-V_{2}}{5}+frac{V_{3}}{4}+frac{V_{3}+V_{2}*10}{3}=0

$$\frac { V _ { 3 } - V _ { 2 } } { 5 } + \frac { V _ { 3 } } { 4 } + \frac { V _ { 3 } + V _ { 2 } \times 10 } { 3 } = 0$$

Solve for V_2

$$V_{2}=-\frac{V_{3}}{4}$$

Steps for Solving Linear Equation

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

$$12\left(V_{3}-V_{2}\right)+15V_{3}+20\left(V_{3}+V_{2}\times 10\right)=0$$

Use the distributive property to multiply 12 by V_{3}-V_{2}.

$$12V_{3}-12V_{2}+15V_{3}+20\left(V_{3}+V_{2}\times 10\right)=0$$

Combine 12V_{3} and 15V_{3} to get 27V_{3}.

$$27V_{3}-12V_{2}+20\left(V_{3}+V_{2}\times 10\right)=0$$

Use the distributive property to multiply 20 by V_{3}+V_{2}\times 10.

$$27V_{3}-12V_{2}+20V_{3}+20V_{2}\times 10=0$$

Multiply 20 and 10 to get 200.

$$27V_{3}-12V_{2}+20V_{3}+200V_{2}=0$$

Combine 27V_{3} and 20V_{3} to get 47V_{3}.

$$47V_{3}-12V_{2}+200V_{2}=0$$

Combine -12V_{2} and 200V_{2} to get 188V_{2}.

$$47V_{3}+188V_{2}=0$$

Subtract 47V_{3} from both sides. Anything subtracted from zero gives its negation.

$$188V_{2}=-47V_{3}$$

Divide both sides by 188.

$$\frac{188V_{2}}{188}=-\frac{47V_{3}}{188}$$

Dividing by 188 undoes the multiplication by 188.

$$V_{2}=-\frac{47V_{3}}{188}$$

Divide -47V_{3} by 188.

$$V_{2}=-\frac{V_{3}}{4}$$

Solve for V_3

$$V_{3}=-4V_{2}$$

Steps for Solving Linear Equation

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

$$12\left(V_{3}-V_{2}\right)+15V_{3}+20\left(V_{3}+V_{2}\times 10\right)=0$$

Use the distributive property to multiply 12 by V_{3}-V_{2}.

$$12V_{3}-12V_{2}+15V_{3}+20\left(V_{3}+V_{2}\times 10\right)=0$$

Combine 12V_{3} and 15V_{3} to get 27V_{3}.

$$27V_{3}-12V_{2}+20\left(V_{3}+V_{2}\times 10\right)=0$$

Use the distributive property to multiply 20 by V_{3}+V_{2}\times 10.

$$27V_{3}-12V_{2}+20V_{3}+20V_{2}\times 10=0$$

Multiply 20 and 10 to get 200.

$$27V_{3}-12V_{2}+20V_{3}+200V_{2}=0$$

Combine 27V_{3} and 20V_{3} to get 47V_{3}.

$$47V_{3}-12V_{2}+200V_{2}=0$$

Combine -12V_{2} and 200V_{2} to get 188V_{2}.

$$47V_{3}+188V_{2}=0$$

Subtract 188V_{2} from both sides. Anything subtracted from zero gives its negation.

$$47V_{3}=-188V_{2}$$

Divide both sides by 47.

$$\frac{47V_{3}}{47}=-\frac{188V_{2}}{47}$$

Dividing by 47 undoes the multiplication by 47.

$$V_{3}=-\frac{188V_{2}}{47}$$

Divide -188V_{2} by 47.

$$V_{3}=-4V_{2}$$