Algebra Examples

$5 x (x - 2) - 3 x = 2 x$

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 $5 x (x - 2) - 3 x$ .

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Step 1.1.1.1

Simplify each term.

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Step 1.1.1.1.1

Apply the distributive property.

$5 x \cdot x + 5 x \cdot - 2 - 3 x = 2 x$

Step 1.1.1.1.2

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

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Step 1.1.1.1.2.1

Move $x$ .

$5 (x \cdot x) + 5 x \cdot - 2 - 3 x = 2 x$

Step 1.1.1.1.2.2

Multiply $x$ by $x$ .

$5 x^{2} + 5 x \cdot - 2 - 3 x = 2 x$

Step 1.1.1.1.3

Multiply $- 2$ by $5$ .

$5 x^{2} - 10 x - 3 x = 2 x$

Step 1.1.1.2

Subtract $3 x$ from $- 10 x$ .

$5 x^{2} - 13 x = 2 x$

Step 1.2

Subtract $2 x$ from both sides of the equation.

$5 x^{2} - 13 x - 2 x = 0$

Step 1.3

Subtract $2 x$ from $- 13 x$ .

$5 x^{2} - 15 x = 0$

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.

$a = 5$ , $b = - 15$ , $c = 0$