Algebra Examples

$(8 - 9 a) a = - 40 + (6 - 3 a) (6 + 3 a)$

Step 1

Simplify $(8 - 9 a) a$ .

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Step 1.1

Rewrite.

$0 + 0 + (8 - 9 a) a = - 40 + (6 - 3 a) (6 + 3 a)$

Step 1.2

Simplify by adding zeros.

$(8 - 9 a) a = - 40 + (6 - 3 a) (6 + 3 a)$

Step 1.3

Apply the distributive property.

$8 a - 9 a \cdot a = - 40 + (6 - 3 a) (6 + 3 a)$

Step 1.4

Multiply $a$ by $a$ by adding the exponents.

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Step 1.4.1

Move $a$ .

$8 a - 9 (a \cdot a) = - 40 + (6 - 3 a) (6 + 3 a)$

Step 1.4.2

Multiply $a$ by $a$ .

$8 a - 9 a^{2} = - 40 + (6 - 3 a) (6 + 3 a)$

Step 2

Simplify $- 40 + (6 - 3 a) (6 + 3 a)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Expand $(6 - 3 a) (6 + 3 a)$ using the FOIL Method.

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Step 2.1.1.1

Apply the distributive property.

$8 a - 9 a^{2} = - 40 + 6 (6 + 3 a) - 3 a (6 + 3 a)$

Step 2.1.1.2

Apply the distributive property.

$8 a - 9 a^{2} = - 40 + 6 \cdot 6 + 6 (3 a) - 3 a (6 + 3 a)$

Step 2.1.1.3

Apply the distributive property.

$8 a - 9 a^{2} = - 40 + 6 \cdot 6 + 6 (3 a) - 3 a \cdot 6 - 3 a (3 a)$

Step 2.1.2

Combine the opposite terms in $6 \cdot 6 + 6 (3 a) - 3 a \cdot 6 - 3 a (3 a)$ .

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Step 2.1.2.1

Reorder the factors in the terms $6 (3 a)$ and $- 3 a \cdot 6$ .

$8 a - 9 a^{2} = - 40 + 6 \cdot 6 + 3 \cdot 6 a - 3 \cdot 6 a - 3 a (3 a)$

Step 2.1.2.2

Subtract $3 \cdot 6 a$ from $3 \cdot 6 a$ .

$8 a - 9 a^{2} = - 40 + 6 \cdot 6 + 0 - 3 a (3 a)$

Step 2.1.2.3

Add $6 \cdot 6$ and $0$ .

$8 a - 9 a^{2} = - 40 + 6 \cdot 6 - 3 a (3 a)$

Step 2.1.3

Simplify each term.

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Step 2.1.3.1

Multiply $6$ by $6$ .

$8 a - 9 a^{2} = - 40 + 36 - 3 a (3 a)$

Step 2.1.3.2

Rewrite using the commutative property of multiplication.

$8 a - 9 a^{2} = - 40 + 36 - 3 \cdot 3 a \cdot a$

Step 2.1.3.3

Multiply $a$ by $a$ by adding the exponents.

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Step 2.1.3.3.1

Move $a$ .

$8 a - 9 a^{2} = - 40 + 36 - 3 \cdot 3 (a \cdot a)$

Step 2.1.3.3.2

Multiply $a$ by $a$ .

$8 a - 9 a^{2} = - 40 + 36 - 3 \cdot 3 a^{2}$

Step 2.1.3.4

Multiply $- 3$ by $3$ .

$8 a - 9 a^{2} = - 40 + 36 - 9 a^{2}$

Step 2.2

Add $- 40$ and $36$ .

$8 a - 9 a^{2} = - 4 - 9 a^{2}$

Step 3

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

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Step 3.1

Add $9 a^{2}$ to both sides of the equation.

$8 a - 9 a^{2} + 9 a^{2} = - 4$

Step 3.2

Combine the opposite terms in $8 a - 9 a^{2} + 9 a^{2}$ .

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Step 3.2.1

Add $- 9 a^{2}$ and $9 a^{2}$ .

$8 a + 0 = - 4$

Step 3.2.2

Add $8 a$ and $0$ .

$8 a = - 4$

Step 4

Divide each term in $8 a = - 4$ by $8$ and simplify.

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Step 4.1

Divide each term in $8 a = - 4$ by $8$ .

$\frac{8 a}{8} = \frac{- 4}{8}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $8$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{8 a}{8} = \frac{- 4}{8}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 4}{8}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 4$ and $8$ .

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Step 4.3.1.1

Factor $4$ out of $- 4$ .

$a = \frac{4 (- 1)}{8}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $4$ out of $8$ .

$a = \frac{4 \cdot - 1}{4 \cdot 2}$

Step 4.3.1.2.2

Cancel the common factor.

$a = \frac{4 \cdot - 1}{4 \cdot 2}$

Step 4.3.1.2.3

Rewrite the expression.

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

Step 4.3.2

Move the negative in front of the fraction.

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

Step 5