Algebra Examples

$(x - 2) (2 x + 4) = 12$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $(x - 2) (2 x + 4)$ .

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Step 1.1.1.1

Expand $(x - 2) (2 x + 4)$ using the FOIL Method.

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Step 1.1.1.1.1

Apply the distributive property.

$x (2 x + 4) - 2 (2 x + 4) = 12$

Step 1.1.1.1.2

Apply the distributive property.

$x (2 x) + x \cdot 4 - 2 (2 x + 4) = 12$

Step 1.1.1.1.3

Apply the distributive property.

$x (2 x) + x \cdot 4 - 2 (2 x) - 2 \cdot 4 = 12$

Step 1.1.1.2

Simplify and combine like terms.

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Step 1.1.1.2.1

Simplify each term.

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Step 1.1.1.2.1.1

Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot 4 - 2 (2 x) - 2 \cdot 4 = 12$

Step 1.1.1.2.1.2

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

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Step 1.1.1.2.1.2.1

Move $x$ .

$2 (x \cdot x) + x \cdot 4 - 2 (2 x) - 2 \cdot 4 = 12$

Step 1.1.1.2.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + x \cdot 4 - 2 (2 x) - 2 \cdot 4 = 12$

Step 1.1.1.2.1.3

Move $4$ to the left of $x$ .

$2 x^{2} + 4 \cdot x - 2 (2 x) - 2 \cdot 4 = 12$

Step 1.1.1.2.1.4

Multiply $2$ by $- 2$ .

$2 x^{2} + 4 x - 4 x - 2 \cdot 4 = 12$

Step 1.1.1.2.1.5

Multiply $- 2$ by $4$ .

$2 x^{2} + 4 x - 4 x - 8 = 12$

Step 1.1.1.2.2

Subtract $4 x$ from $4 x$ .

$2 x^{2} + 0 - 8 = 12$

Step 1.1.1.2.3

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

$2 x^{2} - 8 = 12$

Step 1.2

Subtract $12$ from both sides of the equation.

$2 x^{2} - 8 - 12 = 0$

Step 1.3

Subtract $12$ from $- 8$ .

$2 x^{2} - 20 = 0$

Step 2

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Step 3

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 2$ , $b = 0$ , $c = - 20$