Algebra Examples

$2 x (x - 3) = 15$

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 $2 x (x - 3)$ .

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Step 1.1.1.1

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 3 = 15$

Step 1.1.1.2

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

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Step 1.1.1.2.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 3 = 15$

Step 1.1.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 3 = 15$

Step 1.1.1.3

Multiply $- 3$ by $2$ .

$2 x^{2} - 6 x = 15$

Step 1.2

Subtract $15$ from both sides of the equation.

$2 x^{2} - 6 x - 15 = 0$

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.

$a = 2$ , $b = - 6$ , $c = - 15$