Algebra Examples

$2 x - 5 (x + 3) = x (x - 4)$

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

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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.

$2 x - 5 x - 5 \cdot 3 = x (x - 4)$

Step 1.1.1.1.2

Multiply $- 5$ by $3$ .

$2 x - 5 x - 15 = x (x - 4)$

Step 1.1.1.2

Subtract $5 x$ from $2 x$ .

$- 3 x - 15 = x (x - 4)$

Step 1.2

Simplify the right side.

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Step 1.2.1

Simplify $x (x - 4)$ .

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Step 1.2.1.1

Apply the distributive property.

$- 3 x - 15 = x \cdot x + x \cdot - 4$

Step 1.2.1.2

Simplify the expression.

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Step 1.2.1.2.1

Multiply $x$ by $x$ .

$- 3 x - 15 = x^{2} + x \cdot - 4$

Step 1.2.1.2.2

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

$- 3 x - 15 = x^{2} - 4 x$

Step 1.3

Move all the expressions to the left side of the equation.

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Step 1.3.1

Subtract $x^{2}$ from both sides of the equation.

$- 3 x - 15 - x^{2} = - 4 x$

Step 1.3.2

Add $4 x$ to both sides of the equation.

$- 3 x - 15 - x^{2} + 4 x = 0$

Step 1.4

Add $- 3 x$ and $4 x$ .

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

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.

$a = - 1$ , $b = 1$ , $c = - 15$