Algebra Examples

$(6 x - 1) (6 x + 1) - 4 x (9 x + 2) = - 1$

Step 1

Simplify $(6 x - 1) (6 x + 1) - 4 x (9 x + 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Expand $(6 x - 1) (6 x + 1)$ using the FOIL Method.

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Step 1.1.1.1

Apply the distributive property.

$6 x (6 x + 1) - 1 (6 x + 1) - 4 x (9 x + 2) = - 1$

Step 1.1.1.2

Apply the distributive property.

$6 x (6 x) + 6 x \cdot 1 - 1 (6 x + 1) - 4 x (9 x + 2) = - 1$

Step 1.1.1.3

Apply the distributive property.

$6 x (6 x) + 6 x \cdot 1 - 1 (6 x) - 1 \cdot 1 - 4 x (9 x + 2) = - 1$

Step 1.1.2

Combine the opposite terms in $6 x (6 x) + 6 x \cdot 1 - 1 (6 x) - 1 \cdot 1$ .

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Step 1.1.2.1

Reorder the factors in the terms $6 x \cdot 1$ and $- 1 (6 x)$ .

$6 x (6 x) + 1 \cdot 6 x - 1 \cdot 6 x - 1 \cdot 1 - 4 x (9 x + 2) = - 1$

Step 1.1.2.2

Subtract $6 x$ from $1 \cdot 6 x$ .

$6 x (6 x) + 0 - 1 \cdot 1 - 4 x (9 x + 2) = - 1$

Step 1.1.2.3

Add $6 x (6 x)$ and $0$ .

$6 x (6 x) - 1 \cdot 1 - 4 x (9 x + 2) = - 1$

Step 1.1.3

Simplify each term.

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Step 1.1.3.1

Rewrite using the commutative property of multiplication.

$6 \cdot 6 x \cdot x - 1 \cdot 1 - 4 x (9 x + 2) = - 1$

Step 1.1.3.2

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

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Step 1.1.3.2.1

Move $x$ .

$6 \cdot 6 (x \cdot x) - 1 \cdot 1 - 4 x (9 x + 2) = - 1$

Step 1.1.3.2.2

Multiply $x$ by $x$ .

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

Step 1.1.3.3

Multiply $6$ by $6$ .

$36 x^{2} - 1 \cdot 1 - 4 x (9 x + 2) = - 1$

Step 1.1.3.4

Multiply $- 1$ by $1$ .

$36 x^{2} - 1 - 4 x (9 x + 2) = - 1$

Step 1.1.4

Apply the distributive property.

$36 x^{2} - 1 - 4 x (9 x) - 4 x \cdot 2 = - 1$

Step 1.1.5

Rewrite using the commutative property of multiplication.

$36 x^{2} - 1 - 4 \cdot 9 x \cdot x - 4 x \cdot 2 = - 1$

Step 1.1.6

Multiply $2$ by $- 4$ .

$36 x^{2} - 1 - 4 \cdot 9 x \cdot x - 8 x = - 1$

Step 1.1.7

Simplify each term.

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Step 1.1.7.1

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

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Step 1.1.7.1.1

Move $x$ .

$36 x^{2} - 1 - 4 \cdot 9 (x \cdot x) - 8 x = - 1$

Step 1.1.7.1.2

Multiply $x$ by $x$ .

$36 x^{2} - 1 - 4 \cdot 9 x^{2} - 8 x = - 1$

Step 1.1.7.2

Multiply $- 4$ by $9$ .

$36 x^{2} - 1 - 36 x^{2} - 8 x = - 1$

Step 1.2

Combine the opposite terms in $36 x^{2} - 1 - 36 x^{2} - 8 x$ .

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Step 1.2.1

Subtract $36 x^{2}$ from $36 x^{2}$ .

$0 - 1 - 8 x = - 1$

Step 1.2.2

Subtract $1$ from $0$ .

$- 1 - 8 x = - 1$

Step 2

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

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Step 2.1

Add $1$ to both sides of the equation.

$- 8 x = - 1 + 1$

Step 2.2

Add $- 1$ and $1$ .

$- 8 x = 0$

Step 3

Divide each term in $- 8 x = 0$ by $- 8$ and simplify.

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Step 3.1

Divide each term in $- 8 x = 0$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{0}{- 8}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 8$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{0}{- 8}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{- 8}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $- 8$ .

$x = 0$