Solve for a (8-9a)a=-40+(6-3a)(6+3a)

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

Simplify $(8 - 9 a) a$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

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

Simplify each term.

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

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

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

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

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

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

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

Simplify each term.

Multiply $6$ by $6$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $- 3$ by $3$ .

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

Add $- 40$ and $36$ .

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

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

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

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

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

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

$8 a + 0 = - 4$

Add $8 a$ and $0$ .

$8 a = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

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

Divide $a$ by $1$ .

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

Simplify the right side.

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

Factor $4$ out of $- 4$ .

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

Cancel the common factors.

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = - 0.5$

Solve for a (8-9a)a=-40+(6-3a)(6+3a)

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