Algebra Examples

$\frac{m}{3} = \frac{m^{2}}{6}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$m \cdot 6 = 3 m^{2}$

Step 2

Solve the equation for $m$ .

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Step 2.1

Move $6$ to the left of $m$ .

$6 m = 3 m^{2}$

Step 2.2

Subtract $3 m^{2}$ from both sides of the equation.

$6 m - 3 m^{2} = 0$

Step 2.3

Factor the left side of the equation.

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Step 2.3.1

Let $u = m$ . Substitute $u$ for all occurrences of $m$ .

$6 u - 3 u^{2} = 0$

Step 2.3.2

Factor $3 u$ out of $6 u - 3 u^{2}$ .

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Step 2.3.2.1

Factor $3 u$ out of $6 u$ .

$3 u (2) - 3 u^{2} = 0$

Step 2.3.2.2

Factor $3 u$ out of $- 3 u^{2}$ .

$3 u (2) + 3 u (- u) = 0$

Step 2.3.2.3

Factor $3 u$ out of $3 u (2) + 3 u (- u)$ .

$3 u (2 - u) = 0$

Step 2.3.3

Replace all occurrences of $u$ with $m$ .

$3 m (2 - m) = 0$

Step 2.4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$m = 0$

$2 - m = 0$

Step 2.5

Set $m$ equal to $0$ .

$m = 0$

Step 2.6

Set $2 - m$ equal to $0$ and solve for $m$ .

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Step 2.6.1

Set $2 - m$ equal to $0$ .

$2 - m = 0$

Step 2.6.2

Solve $2 - m = 0$ for $m$ .

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Step 2.6.2.1

Subtract $2$ from both sides of the equation.

$- m = - 2$

Step 2.6.2.2

Divide each term in $- m = - 2$ by $- 1$ and simplify.

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Step 2.6.2.2.1

Divide each term in $- m = - 2$ by $- 1$ .

$\frac{- m}{- 1} = \frac{- 2}{- 1}$

Step 2.6.2.2.2

Simplify the left side.

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Step 2.6.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{m}{1} = \frac{- 2}{- 1}$

Step 2.6.2.2.2.2

Divide $m$ by $1$ .

$m = \frac{- 2}{- 1}$

Step 2.6.2.2.3

Simplify the right side.

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Step 2.6.2.2.3.1

Divide $- 2$ by $- 1$ .

$m = 2$

Step 2.7

The final solution is all the values that make $3 m (2 - m) = 0$ true.

$m = 0, 2$