Basic Math Examples

$4 (y - 6) - 6 = - 3 (- 6 y + 8) - 5 y$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 3 (- 6 y + 8) - 5 y = 4 (y - 6) - 6$

Step 2

Simplify $- 3 (- 6 y + 8) - 5 y$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 3 (- 6 y) - 3 \cdot 8 - 5 y = 4 (y - 6) - 6$

Step 2.1.2

Multiply $- 6$ by $- 3$ .

$18 y - 3 \cdot 8 - 5 y = 4 (y - 6) - 6$

Step 2.1.3

Multiply $- 3$ by $8$ .

$18 y - 24 - 5 y = 4 (y - 6) - 6$

Step 2.2

Subtract $5 y$ from $18 y$ .

$13 y - 24 = 4 (y - 6) - 6$

Step 3

Simplify $4 (y - 6) - 6$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$13 y - 24 = 4 y + 4 \cdot - 6 - 6$

Step 3.1.2

Multiply $4$ by $- 6$ .

$13 y - 24 = 4 y - 24 - 6$

Step 3.2

Subtract $6$ from $- 24$ .

$13 y - 24 = 4 y - 30$

Step 4

Move all terms containing $y$ to the left side of the equation.

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Step 4.1

Subtract $4 y$ from both sides of the equation.

$13 y - 24 - 4 y = - 30$

Step 4.2

Subtract $4 y$ from $13 y$ .

$9 y - 24 = - 30$

Step 5

Move all terms not containing $y$ to the right side of the equation.

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Step 5.1

Add $24$ to both sides of the equation.

$9 y = - 30 + 24$

Step 5.2

Add $- 30$ and $24$ .

$9 y = - 6$

Step 6

Divide each term in $9 y = - 6$ by $9$ and simplify.

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Step 6.1

Divide each term in $9 y = - 6$ by $9$ .

$\frac{9 y}{9} = \frac{- 6}{9}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $9$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 6}{9}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 6}{9}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of $- 6$ and $9$ .

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Step 6.3.1.1

Factor $3$ out of $- 6$ .

$y = \frac{3 (- 2)}{9}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $3$ out of $9$ .

$y = \frac{3 \cdot - 2}{3 \cdot 3}$

Step 6.3.1.2.2

Cancel the common factor.

$y = \frac{3 \cdot - 2}{3 \cdot 3}$

Step 6.3.1.2.3

Rewrite the expression.

$y = \frac{- 2}{3}$

Step 6.3.2

Move the negative in front of the fraction.

$y = - \frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{2}{3}$

Decimal Form:

$y = - 0.\overline{6}$