Basic Math Examples

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

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.

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

Step 2

Simplify $6 y + 3 (4 y - 3)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$6 y + 3 (4 y) + 3 \cdot - 3 = 6 + 3 (4 - 3 y)$

Step 2.1.2

Multiply $4$ by $3$ .

$6 y + 12 y + 3 \cdot - 3 = 6 + 3 (4 - 3 y)$

Step 2.1.3

Multiply $3$ by $- 3$ .

$6 y + 12 y - 9 = 6 + 3 (4 - 3 y)$

Step 2.2

Add $6 y$ and $12 y$ .

$18 y - 9 = 6 + 3 (4 - 3 y)$

Step 3

Simplify $6 + 3 (4 - 3 y)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$18 y - 9 = 6 + 3 \cdot 4 + 3 (- 3 y)$

Step 3.1.2

Multiply $3$ by $4$ .

$18 y - 9 = 6 + 12 + 3 (- 3 y)$

Step 3.1.3

Multiply $- 3$ by $3$ .

$18 y - 9 = 6 + 12 - 9 y$

Step 3.2

Add $6$ and $12$ .

$18 y - 9 = 18 - 9 y$

Step 4

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

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Step 4.1

Add $9 y$ to both sides of the equation.

$18 y - 9 + 9 y = 18$

Step 4.2

Add $18 y$ and $9 y$ .

$27 y - 9 = 18$

Step 5

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

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Step 5.1

Add $9$ to both sides of the equation.

$27 y = 18 + 9$

Step 5.2

Add $18$ and $9$ .

$27 y = 27$

Step 6

Divide each term in $27 y = 27$ by $27$ and simplify.

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Step 6.1

Divide each term in $27 y = 27$ by $27$ .

$\frac{27 y}{27} = \frac{27}{27}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $27$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{27 y}{27} = \frac{27}{27}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{27}{27}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $27$ by $27$ .

$y = 1$