Algebra Examples

$(1 - 2 x) (1 - 3 x) = (6 x - 1) x - 1$

Step 1

Simplify $(1 - 2 x) (1 - 3 x)$ .

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Step 1.1

Rewrite.

$0 + 0 + (1 - 2 x) (1 - 3 x) = (6 x - 1) x - 1$

Step 1.2

Simplify by adding zeros.

$(1 - 2 x) (1 - 3 x) = (6 x - 1) x - 1$

Step 1.3

Expand $(1 - 2 x) (1 - 3 x)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$1 (1 - 3 x) - 2 x (1 - 3 x) = (6 x - 1) x - 1$

Step 1.3.2

Apply the distributive property.

$1 \cdot 1 + 1 (- 3 x) - 2 x (1 - 3 x) = (6 x - 1) x - 1$

Step 1.3.3

Apply the distributive property.

$1 \cdot 1 + 1 (- 3 x) - 2 x \cdot 1 - 2 x (- 3 x) = (6 x - 1) x - 1$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $1$ by $1$ .

$1 + 1 (- 3 x) - 2 x \cdot 1 - 2 x (- 3 x) = (6 x - 1) x - 1$

Step 1.4.1.2

Multiply $- 3 x$ by $1$ .

$1 - 3 x - 2 x \cdot 1 - 2 x (- 3 x) = (6 x - 1) x - 1$

Step 1.4.1.3

Multiply $- 2$ by $1$ .

$1 - 3 x - 2 x - 2 x (- 3 x) = (6 x - 1) x - 1$

Step 1.4.1.4

Rewrite using the commutative property of multiplication.

$1 - 3 x - 2 x - 2 \cdot - 3 x \cdot x = (6 x - 1) x - 1$

Step 1.4.1.5

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

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Step 1.4.1.5.1

Move $x$ .

$1 - 3 x - 2 x - 2 \cdot - 3 (x \cdot x) = (6 x - 1) x - 1$

Step 1.4.1.5.2

Multiply $x$ by $x$ .

$1 - 3 x - 2 x - 2 \cdot - 3 x^{2} = (6 x - 1) x - 1$

Step 1.4.1.6

Multiply $- 2$ by $- 3$ .

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

Step 1.4.2

Subtract $2 x$ from $- 3 x$ .

$1 - 5 x + 6 x^{2} = (6 x - 1) x - 1$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$1 - 5 x + 6 x^{2} = 6 x \cdot x - 1 x - 1$

Step 2.2

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

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Step 2.2.1

Move $x$ .

$1 - 5 x + 6 x^{2} = 6 (x \cdot x) - 1 x - 1$

Step 2.2.2

Multiply $x$ by $x$ .

$1 - 5 x + 6 x^{2} = 6 x^{2} - 1 x - 1$

Step 2.3

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

$1 - 5 x + 6 x^{2} = 6 x^{2} - x - 1$

Step 3

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

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Step 3.1

Subtract $6 x^{2}$ from both sides of the equation.

$1 - 5 x + 6 x^{2} - 6 x^{2} = - x - 1$

Step 3.2

Add $x$ to both sides of the equation.

$1 - 5 x + 6 x^{2} - 6 x^{2} + x = - 1$

Step 3.3

Combine the opposite terms in $1 - 5 x + 6 x^{2} - 6 x^{2} + x$ .

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Step 3.3.1

Subtract $6 x^{2}$ from $6 x^{2}$ .

$1 - 5 x + 0 + x = - 1$

Step 3.3.2

Add $1 - 5 x$ and $0$ .

$1 - 5 x + x = - 1$

Step 3.4

Add $- 5 x$ and $x$ .

$1 - 4 x = - 1$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$- 4 x = - 1 - 1$

Step 4.2

Subtract $1$ from $- 1$ .

$- 4 x = - 2$

Step 5

Divide each term in $- 4 x = - 2$ by $- 4$ and simplify.

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Step 5.1

Divide each term in $- 4 x = - 2$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 2}{- 4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 2}{- 4}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{- 4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 2$ and $- 4$ .

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Step 5.3.1.1

Factor $- 2$ out of $- 2$ .

$x = \frac{- 2 (1)}{- 4}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $- 2$ out of $- 4$ .

$x = \frac{- 2 \cdot 1}{- 2 \cdot 2}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{- 2 \cdot 1}{- 2 \cdot 2}$

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$