Algebra Examples

$12 - x (x - 3) = (6 - x) (x + 2)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$12 - x \cdot x - x \cdot - 3 = (6 - x) (x + 2)$

Step 1.2

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

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Step 1.2.1

Move $x$ .

$12 - (x \cdot x) - x \cdot - 3 = (6 - x) (x + 2)$

Step 1.2.2

Multiply $x$ by $x$ .

$12 - x^{2} - x \cdot - 3 = (6 - x) (x + 2)$

Step 1.3

Multiply $- 3$ by $- 1$ .

$12 - x^{2} + 3 x = (6 - x) (x + 2)$

Step 2

Simplify $(6 - x) (x + 2)$ .

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Step 2.1

Expand $(6 - x) (x + 2)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$12 - x^{2} + 3 x = 6 (x + 2) - x (x + 2)$

Step 2.1.2

Apply the distributive property.

$12 - x^{2} + 3 x = 6 x + 6 \cdot 2 - x (x + 2)$

Step 2.1.3

Apply the distributive property.

$12 - x^{2} + 3 x = 6 x + 6 \cdot 2 - x \cdot x - x \cdot 2$

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 $6$ by $2$ .

$12 - x^{2} + 3 x = 6 x + 12 - x \cdot x - x \cdot 2$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x$ .

$12 - x^{2} + 3 x = 6 x + 12 - (x \cdot x) - x \cdot 2$

Step 2.2.1.2.2

Multiply $x$ by $x$ .

$12 - x^{2} + 3 x = 6 x + 12 - x^{2} - x \cdot 2$

Step 2.2.1.3

Multiply $2$ by $- 1$ .

$12 - x^{2} + 3 x = 6 x + 12 - x^{2} - 2 x$

Step 2.2.2

Subtract $2 x$ from $6 x$ .

$12 - x^{2} + 3 x = 4 x + 12 - x^{2}$

Step 3

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

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Step 3.1

Subtract $4 x$ from both sides of the equation.

$12 - x^{2} + 3 x - 4 x = 12 - x^{2}$

Step 3.2

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

$12 - x^{2} + 3 x - 4 x + x^{2} = 12$

Step 3.3

Combine the opposite terms in $12 - x^{2} + 3 x - 4 x + x^{2}$ .

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Step 3.3.1

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

$12 + 3 x - 4 x + 0 = 12$

Step 3.3.2

Add $12 + 3 x - 4 x$ and $0$ .

$12 + 3 x - 4 x = 12$

Step 3.4

Subtract $4 x$ from $3 x$ .

$12 - x = 12$

Step 4

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

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Step 4.1

Subtract $12$ from both sides of the equation.

$- x = 12 - 12$

Step 4.2

Subtract $12$ from $12$ .

$- x = 0$

Step 5

Divide each term in $- x = 0$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- x = 0$ by $- 1$ .

$\frac{- x}{- 1} = \frac{0}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{0}{- 1}$

Step 5.2.2

Divide $x$ by $1$ .

$x = \frac{0}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $- 1$ .

$x = 0$