Solve for x 2^((x-1)(x+2)(x-7)(x+8))=1

$2^{(x - 1) (x + 2) (x - 7) (x + 8)} = 1$

Simplify $2^{(x - 1) (x + 2) (x - 7) (x + 8)}$ .

Expand $(x - 1) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$2^{(x (x + 2) - 1 (x + 2)) (x - 7) (x + 8)} = 1$

Apply the distributive property.

$2^{(x \cdot x + x \cdot 2 - 1 (x + 2)) (x - 7) (x + 8)} = 1$

Apply the distributive property.

$2^{(x \cdot x + x \cdot 2 - 1 x - 1 \cdot 2) (x - 7) (x + 8)} = 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$2^{(x^{2} + x \cdot 2 - 1 x - 1 \cdot 2) (x - 7) (x + 8)} = 1$

Move $2$ to the left of $x$ .

$2^{(x^{2} + 2 \cdot x - 1 x - 1 \cdot 2) (x - 7) (x + 8)} = 1$

Rewrite $- 1 x$ as $- x$ .

$2^{(x^{2} + 2 x - x - 1 \cdot 2) (x - 7) (x + 8)} = 1$

Multiply $- 1$ by $2$ .

$2^{(x^{2} + 2 x - x - 2) (x - 7) (x + 8)} = 1$

Subtract $x$ from $2 x$ .

$2^{(x^{2} + x - 2) (x - 7) (x + 8)} = 1$

Expand $(x^{2} + x - 2) (x - 7)$ by multiplying each term in the first expression by each term in the second expression.

$2^{(x^{2} x + x^{2} \cdot - 7 + x \cdot x + x \cdot - 7 - 2 x - 2 \cdot - 7) (x + 8)} = 1$

Simplify terms.

Simplify each term.

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$2^{(x^{2} x^{1} + x^{2} \cdot - 7 + x \cdot x + x \cdot - 7 - 2 x - 2 \cdot - 7) (x + 8)} = 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{(x^{2 + 1} + x^{2} \cdot - 7 + x \cdot x + x \cdot - 7 - 2 x - 2 \cdot - 7) (x + 8)} = 1$

Add $2$ and $1$ .

$2^{(x^{3} + x^{2} \cdot - 7 + x \cdot x + x \cdot - 7 - 2 x - 2 \cdot - 7) (x + 8)} = 1$

Move $- 7$ to the left of $x^{2}$ .

$2^{(x^{3} - 7 \cdot x^{2} + x \cdot x + x \cdot - 7 - 2 x - 2 \cdot - 7) (x + 8)} = 1$

Multiply $x$ by $x$ .

$2^{(x^{3} - 7 x^{2} + x^{2} + x \cdot - 7 - 2 x - 2 \cdot - 7) (x + 8)} = 1$

Move $- 7$ to the left of $x$ .

$2^{(x^{3} - 7 x^{2} + x^{2} - 7 \cdot x - 2 x - 2 \cdot - 7) (x + 8)} = 1$

Multiply $- 2$ by $- 7$ .

$2^{(x^{3} - 7 x^{2} + x^{2} - 7 x - 2 x + 14) (x + 8)} = 1$

Simplify by adding terms.

Add $- 7 x^{2}$ and $x^{2}$ .

$2^{(x^{3} - 6 x^{2} - 7 x - 2 x + 14) (x + 8)} = 1$

Subtract $2 x$ from $- 7 x$ .

$2^{(x^{3} - 6 x^{2} - 9 x + 14) (x + 8)} = 1$

Expand $(x^{3} - 6 x^{2} - 9 x + 14) (x + 8)$ by multiplying each term in the first expression by each term in the second expression.

$2^{x^{3} x + x^{3} \cdot 8 - 6 x^{2} x - 6 x^{2} \cdot 8 - 9 x \cdot x - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Simplify terms.

Simplify each term.

Multiply $x^{3}$ by $x$ by adding the exponents.

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$2^{x^{3} x^{1} + x^{3} \cdot 8 - 6 x^{2} x - 6 x^{2} \cdot 8 - 9 x \cdot x - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{x^{3 + 1} + x^{3} \cdot 8 - 6 x^{2} x - 6 x^{2} \cdot 8 - 9 x \cdot x - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Add $3$ and $1$ .

$2^{x^{4} + x^{3} \cdot 8 - 6 x^{2} x - 6 x^{2} \cdot 8 - 9 x \cdot x - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Move $8$ to the left of $x^{3}$ .

$2^{x^{4} + 8 \cdot x^{3} - 6 x^{2} x - 6 x^{2} \cdot 8 - 9 x \cdot x - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$2^{x^{4} + 8 x^{3} - 6 (x \cdot x^{2}) - 6 x^{2} \cdot 8 - 9 x \cdot x - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$2^{x^{4} + 8 x^{3} - 6 (x^{1} x^{2}) - 6 x^{2} \cdot 8 - 9 x \cdot x - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{x^{4} + 8 x^{3} - 6 x^{1 + 2} - 6 x^{2} \cdot 8 - 9 x \cdot x - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Add $1$ and $2$ .

$2^{x^{4} + 8 x^{3} - 6 x^{3} - 6 x^{2} \cdot 8 - 9 x \cdot x - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Multiply $8$ by $- 6$ .

$2^{x^{4} + 8 x^{3} - 6 x^{3} - 48 x^{2} - 9 x \cdot x - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2^{x^{4} + 8 x^{3} - 6 x^{3} - 48 x^{2} - 9 (x \cdot x) - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Multiply $x$ by $x$ .

$2^{x^{4} + 8 x^{3} - 6 x^{3} - 48 x^{2} - 9 x^{2} - 9 x \cdot 8 + 14 x + 14 \cdot 8} = 1$

Multiply $8$ by $- 9$ .

$2^{x^{4} + 8 x^{3} - 6 x^{3} - 48 x^{2} - 9 x^{2} - 72 x + 14 x + 14 \cdot 8} = 1$

Multiply $14$ by $8$ .

$2^{x^{4} + 8 x^{3} - 6 x^{3} - 48 x^{2} - 9 x^{2} - 72 x + 14 x + 112} = 1$

Simplify by adding terms.

Subtract $6 x^{3}$ from $8 x^{3}$ .

$2^{x^{4} + 2 x^{3} - 48 x^{2} - 9 x^{2} - 72 x + 14 x + 112} = 1$

Subtract $9 x^{2}$ from $- 48 x^{2}$ .

$2^{x^{4} + 2 x^{3} - 57 x^{2} - 72 x + 14 x + 112} = 1$

Add $- 72 x$ and $14 x$ .

$2^{x^{4} + 2 x^{3} - 57 x^{2} - 58 x + 112} = 1$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - 8, - 2, 1, 7$

Solve for x 2^((x-1)(x+2)(x-7)(x+8))=1

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