Algebra Examples

$3 y (4 y - 1) - 2 y (6 y - 5) = 9 y - 8 (3 + y)$

Step 1

Simplify $3 y (4 y - 1) - 2 y (6 y - 5)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 y (4 y) + 3 y \cdot - 1 - 2 y (6 y - 5) = 9 y - 8 (3 + y)$

Step 1.1.2

Rewrite using the commutative property of multiplication.

$3 \cdot 4 y \cdot y + 3 y \cdot - 1 - 2 y (6 y - 5) = 9 y - 8 (3 + y)$

Step 1.1.3

Multiply $- 1$ by $3$ .

$3 \cdot 4 y \cdot y - 3 y - 2 y (6 y - 5) = 9 y - 8 (3 + y)$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

Multiply $y$ by $y$ by adding the exponents.

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Step 1.1.4.1.1

Move $y$ .

$3 \cdot 4 (y \cdot y) - 3 y - 2 y (6 y - 5) = 9 y - 8 (3 + y)$

Step 1.1.4.1.2

Multiply $y$ by $y$ .

$3 \cdot 4 y^{2} - 3 y - 2 y (6 y - 5) = 9 y - 8 (3 + y)$

Step 1.1.4.2

Multiply $3$ by $4$ .

$12 y^{2} - 3 y - 2 y (6 y - 5) = 9 y - 8 (3 + y)$

Step 1.1.5

Apply the distributive property.

$12 y^{2} - 3 y - 2 y (6 y) - 2 y \cdot - 5 = 9 y - 8 (3 + y)$

Step 1.1.6

Rewrite using the commutative property of multiplication.

$12 y^{2} - 3 y - 2 \cdot 6 y \cdot y - 2 y \cdot - 5 = 9 y - 8 (3 + y)$

Step 1.1.7

Multiply $- 5$ by $- 2$ .

$12 y^{2} - 3 y - 2 \cdot 6 y \cdot y + 10 y = 9 y - 8 (3 + y)$

Step 1.1.8

Simplify each term.

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Step 1.1.8.1

Multiply $y$ by $y$ by adding the exponents.

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Step 1.1.8.1.1

Move $y$ .

$12 y^{2} - 3 y - 2 \cdot 6 (y \cdot y) + 10 y = 9 y - 8 (3 + y)$

Step 1.1.8.1.2

Multiply $y$ by $y$ .

$12 y^{2} - 3 y - 2 \cdot 6 y^{2} + 10 y = 9 y - 8 (3 + y)$

Step 1.1.8.2

Multiply $- 2$ by $6$ .

$12 y^{2} - 3 y - 12 y^{2} + 10 y = 9 y - 8 (3 + y)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $12 y^{2} - 3 y - 12 y^{2} + 10 y$ .

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Step 1.2.1.1

Subtract $12 y^{2}$ from $12 y^{2}$ .

$- 3 y + 0 + 10 y = 9 y - 8 (3 + y)$

Step 1.2.1.2

Add $- 3 y$ and $0$ .

$- 3 y + 10 y = 9 y - 8 (3 + y)$

Step 1.2.2

Add $- 3 y$ and $10 y$ .

$7 y = 9 y - 8 (3 + y)$

Step 2

Simplify $9 y - 8 (3 + y)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$7 y = 9 y - 8 \cdot 3 - 8 y$

Step 2.1.2

Multiply $- 8$ by $3$ .

$7 y = 9 y - 24 - 8 y$

Step 2.2

Subtract $8 y$ from $9 y$ .

$7 y = y - 24$

Step 3

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

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Step 3.1

Subtract $y$ from both sides of the equation.

$7 y - y = - 24$

Step 3.2

Subtract $y$ from $7 y$ .

$6 y = - 24$

Step 4

Divide each term in $6 y = - 24$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 y = - 24$ by $6$ .

$\frac{6 y}{6} = \frac{- 24}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 24}{6}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 24}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 24$ by $6$ .

$y = - 4$