Basic Math Examples

$y = 6 v (\frac{l + 3 a}{g - 2 a})$

Step 1

Rewrite the equation as $6 v (\frac{l + 3 a}{g - 2 a}) = y$ .

$6 v (\frac{l + 3 a}{g - 2 a}) = y$

Step 2

Simplify $6 v (\frac{l + 3 a}{g - 2 a})$ .

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Step 2.1

Multiply $6 v (\frac{l + 3 a}{g - 2 a})$ .

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Step 2.1.1

Combine $6$ and $\frac{l + 3 a}{g - 2 a}$ .

$v \frac{6 (l + 3 a)}{g - 2 a} = y$

Step 2.1.2

Combine $v$ and $\frac{6 (l + 3 a)}{g - 2 a}$ .

$\frac{v (6 (l + 3 a))}{g - 2 a} = y$

Step 2.2

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

$\frac{6 v (l + 3 a)}{g - 2 a} = y$

Step 3

Multiply both sides by $g - 2 a$ .

$\frac{6 v (l + 3 a)}{g - 2 a} (g - 2 a) = y (g - 2 a)$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{6 v (l + 3 a)}{g - 2 a} (g - 2 a)$ .

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Step 4.1.1.1

Cancel the common factor of $g - 2 a$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{6 v (l + 3 a)}{g - 2 a} (g - 2 a) = y (g - 2 a)$

Step 4.1.1.1.2

Rewrite the expression.

$6 v (l + 3 a) = y (g - 2 a)$

Step 4.1.1.2

Apply the distributive property.

$6 v l + 6 v (3 a) = y (g - 2 a)$

Step 4.1.1.3

Simplify the expression.

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Step 4.1.1.3.1

Rewrite using the commutative property of multiplication.

$6 v l + 6 \cdot 3 v a = y (g - 2 a)$

Step 4.1.1.3.2

Multiply $6$ by $3$ .

$6 v l + 18 v a = y (g - 2 a)$

Step 4.1.1.3.3

Move $v$ .

$6 l v + 18 v a = y (g - 2 a)$

Step 4.1.1.3.4

Move $v$ .

$6 l v + 18 a v = y (g - 2 a)$

Step 4.1.1.3.5

Reorder $6 l v$ and $18 a v$ .

$18 a v + 6 l v = y (g - 2 a)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $y (g - 2 a)$ .

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Step 4.2.1.1

Apply the distributive property.

$18 a v + 6 l v = y g + y (- 2 a)$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Rewrite using the commutative property of multiplication.

$18 a v + 6 l v = y g - 2 y a$

Step 4.2.1.2.2

Reorder $y$ and $g$ .

$18 a v + 6 l v = g y - 2 y a$

Step 4.2.1.2.3

Move $y$ .

$18 a v + 6 l v = g y - 2 a y$

Step 4.2.1.2.4

Reorder $g y$ and $- 2 a y$ .

$18 a v + 6 l v = - 2 a y + g y$

Step 5

Solve for $l$ .

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Step 5.1

Subtract $18 a v$ from both sides of the equation.

$6 l v = - 2 a y + g y - 18 a v$

Step 5.2

Divide each term in $6 l v = - 2 a y + g y - 18 a v$ by $6 v$ and simplify.

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Step 5.2.1

Divide each term in $6 l v = - 2 a y + g y - 18 a v$ by $6 v$ .

$\frac{6 l v}{6 v} = \frac{- 2 a y}{6 v} + \frac{g y}{6 v} + \frac{- 18 a v}{6 v}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $6$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{6 l v}{6 v} = \frac{- 2 a y}{6 v} + \frac{g y}{6 v} + \frac{- 18 a v}{6 v}$

Step 5.2.2.1.2

Rewrite the expression.

$\frac{l v}{v} = \frac{- 2 a y}{6 v} + \frac{g y}{6 v} + \frac{- 18 a v}{6 v}$

Step 5.2.2.2

Cancel the common factor of $v$ .

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Step 5.2.2.2.1

Cancel the common factor.

$\frac{l v}{v} = \frac{- 2 a y}{6 v} + \frac{g y}{6 v} + \frac{- 18 a v}{6 v}$

Step 5.2.2.2.2

Divide $l$ by $1$ .

$l = \frac{- 2 a y}{6 v} + \frac{g y}{6 v} + \frac{- 18 a v}{6 v}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Simplify each term.

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Step 5.2.3.1.1

Cancel the common factor of $- 2$ and $6$ .

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Step 5.2.3.1.1.1

Factor $2$ out of $- 2 a y$ .

$l = \frac{2 (- a y)}{6 v} + \frac{g y}{6 v} + \frac{- 18 a v}{6 v}$

Step 5.2.3.1.1.2

Cancel the common factors.

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Step 5.2.3.1.1.2.1

Factor $2$ out of $6 v$ .

$l = \frac{2 (- a y)}{2 (3 v)} + \frac{g y}{6 v} + \frac{- 18 a v}{6 v}$

Step 5.2.3.1.1.2.2

Cancel the common factor.

$l = \frac{2 (- a y)}{2 (3 v)} + \frac{g y}{6 v} + \frac{- 18 a v}{6 v}$

Step 5.2.3.1.1.2.3

Rewrite the expression.

$l = \frac{- a y}{3 v} + \frac{g y}{6 v} + \frac{- 18 a v}{6 v}$

Step 5.2.3.1.2

Move the negative in front of the fraction.

$l = - \frac{a y}{3 v} + \frac{g y}{6 v} + \frac{- 18 a v}{6 v}$

Step 5.2.3.1.3

Cancel the common factor of $- 18$ and $6$ .

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Step 5.2.3.1.3.1

Factor $6$ out of $- 18 a v$ .

$l = - \frac{a y}{3 v} + \frac{g y}{6 v} + \frac{6 (- 3 a v)}{6 v}$

Step 5.2.3.1.3.2

Cancel the common factors.

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Step 5.2.3.1.3.2.1

Factor $6$ out of $6 v$ .

$l = - \frac{a y}{3 v} + \frac{g y}{6 v} + \frac{6 (- 3 a v)}{6 (v)}$

Step 5.2.3.1.3.2.2

Cancel the common factor.

$l = - \frac{a y}{3 v} + \frac{g y}{6 v} + \frac{6 (- 3 a v)}{6 v}$

Step 5.2.3.1.3.2.3

Rewrite the expression.

$l = - \frac{a y}{3 v} + \frac{g y}{6 v} + \frac{- 3 a v}{v}$

Step 5.2.3.1.4

Cancel the common factor of $v$ .

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Step 5.2.3.1.4.1

Cancel the common factor.

$l = - \frac{a y}{3 v} + \frac{g y}{6 v} + \frac{- 3 a v}{v}$

Step 5.2.3.1.4.2

Divide $- 3 a$ by $1$ .

$l = - \frac{a y}{3 v} + \frac{g y}{6 v} - 3 a$