Algebra Examples

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

Step 1

Simplify $x (3 x - 2)$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Reorder.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.2.2.2

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

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

Step 1.3

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

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Step 1.3.1

Move $x$ .

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

Step 1.3.2

Multiply $x$ by $x$ .

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

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

Step 2

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

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Step 2.1

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

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Apply the distributive property.

$3 x^{2} - 2 x = 3 x \cdot x + 3 x \cdot - 3 + 1 x + 1 \cdot - 3$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

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

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Step 2.2.1.1.1

Move $x$ .

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

Step 2.2.1.1.2

Multiply $x$ by $x$ .

$3 x^{2} - 2 x = 3 x^{2} + 3 x \cdot - 3 + 1 x + 1 \cdot - 3$

Step 2.2.1.2

Multiply $- 3$ by $3$ .

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

Step 2.2.1.3

Multiply $x$ by $1$ .

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

Step 2.2.1.4

Multiply $- 3$ by $1$ .

$3 x^{2} - 2 x = 3 x^{2} - 9 x + x - 3$

Step 2.2.2

Add $- 9 x$ and $x$ .

$3 x^{2} - 2 x = 3 x^{2} - 8 x - 3$

Step 3

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

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Step 3.1

Subtract $3 x^{2}$ from both sides of the equation.

$3 x^{2} - 2 x - 3 x^{2} = - 8 x - 3$

Step 3.2

Add $8 x$ to both sides of the equation.

$3 x^{2} - 2 x - 3 x^{2} + 8 x = - 3$

Step 3.3

Combine the opposite terms in $3 x^{2} - 2 x - 3 x^{2} + 8 x$ .

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Step 3.3.1

Subtract $3 x^{2}$ from $3 x^{2}$ .

$- 2 x + 0 + 8 x = - 3$

Step 3.3.2

Add $- 2 x$ and $0$ .

$- 2 x + 8 x = - 3$

Step 3.4

Add $- 2 x$ and $8 x$ .

$6 x = - 3$

Step 4

Divide each term in $6 x = - 3$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 x = - 3$ by $6$ .

$\frac{6 x}{6} = \frac{- 3}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 3}{6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 3$ and $6$ .

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Step 4.3.1.1

Factor $3$ out of $- 3$ .

$x = \frac{3 (- 1)}{6}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $3$ out of $6$ .

$x = \frac{3 \cdot - 1}{3 \cdot 2}$

Step 4.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot - 1}{3 \cdot 2}$

Step 4.3.1.2.3

Rewrite the expression.

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

Step 4.3.2

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.5$