Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

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

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Step 1.2.1

Move $x$ .

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

Step 1.2.2

Multiply $x$ by $x$ .

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

Step 1.3

Multiply $- 3$ by $- 2$ .

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

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.

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Apply the distributive property.

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

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 $2$ .

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

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x$ .

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

Step 2.2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.2.1.3

Multiply $2$ by $- 1$ .

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

Step 2.2.2

Subtract $2 x$ from $6 x$ .

$12 - 2 x^{2} + 6 x = 4 x + 12 - x^{2}$

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.

$12 - 2 x^{2} + 6 x - 4 x = 12 - x^{2}$

Step 3.2

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

$12 - 2 x^{2} + 6 x - 4 x + x^{2} = 12$

Step 3.3

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

$12 - x^{2} + 6 x - 4 x = 12$

Step 3.4

Subtract $4 x$ from $6 x$ .

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

Step 4

Subtract $12$ from both sides of the equation.

$12 - x^{2} + 2 x - 12 = 0$

Step 5

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

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Step 5.1

Subtract $12$ from $12$ .

$- x^{2} + 2 x + 0 = 0$

Step 5.2

Add $- x^{2} + 2 x$ and $0$ .

$- x^{2} + 2 x = 0$

Step 6

Factor $- x$ out of $- x^{2} + 2 x$ .

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Step 6.1

Factor $- x$ out of $- x^{2}$ .

$- x \cdot x + 2 x = 0$

Step 6.2

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

$- x \cdot x - x \cdot - 2 = 0$

Step 6.3

Factor $- x$ out of $- x (x) - x (- 2)$ .

$- x (x - 2) = 0$

Step 7

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 2 = 0$

Step 8

Set $x$ equal to $0$ .

$x = 0$

Step 9

Set $x - 2$ equal to $0$ and solve for $x$ .

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Step 9.1

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 9.2

Add $2$ to both sides of the equation.

$x = 2$

Step 10

The final solution is all the values that make $- x (x - 2) = 0$ true.

$x = 0, 2$