Algebra Examples

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

Step 1

Add $2 x$ to both sides of the equation.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Apply the distributive property.

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

Step 2.1.1.3

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 3 - 1 x - 1 \cdot 3 + 2 x = 0$

Step 2.1.2

Simplify and combine like terms.

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Step 2.1.2.1

Simplify each term.

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Step 2.1.2.1.1

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

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Step 2.1.2.1.1.1

Move $x$ .

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

Step 2.1.2.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot 3 - 1 x - 1 \cdot 3 + 2 x = 0$

Step 2.1.2.1.2

Multiply $3$ by $2$ .

$2 x^{2} + 6 x - 1 x - 1 \cdot 3 + 2 x = 0$

Step 2.1.2.1.3

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

$2 x^{2} + 6 x - x - 1 \cdot 3 + 2 x = 0$

Step 2.1.2.1.4

Multiply $- 1$ by $3$ .

$2 x^{2} + 6 x - x - 3 + 2 x = 0$

Step 2.1.2.2

Subtract $x$ from $6 x$ .

$2 x^{2} + 5 x - 3 + 2 x = 0$

Step 2.2

Add $5 x$ and $2 x$ .

$2 x^{2} + 7 x - 3 = 0$

Step 3

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 4

The standard form is $2 x^{2} + 7 x - 3$ .

$2 x^{2} + 7 x - 3 = 0$

Step 5