Algebra Examples

$(2 x + 5) (x - 1) = - 6$

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 $(2 x + 5) (x - 1)$ .

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Step 1.1.1.1

Expand $(2 x + 5) (x - 1)$ using the FOIL Method.

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Step 1.1.1.1.1

Apply the distributive property.

$2 x (x - 1) + 5 (x - 1) = - 6$

Step 1.1.1.1.2

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 1 + 5 (x - 1) = - 6$

Step 1.1.1.1.3

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 1 + 5 x + 5 \cdot - 1 = - 6$

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

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

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Step 1.1.1.2.1.1.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 1 + 5 x + 5 \cdot - 1 = - 6$

Step 1.1.1.2.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 1 + 5 x + 5 \cdot - 1 = - 6$

Step 1.1.1.2.1.2

Multiply $- 1$ by $2$ .

$2 x^{2} - 2 x + 5 x + 5 \cdot - 1 = - 6$

Step 1.1.1.2.1.3

Multiply $5$ by $- 1$ .

$2 x^{2} - 2 x + 5 x - 5 = - 6$

Step 1.1.1.2.2

Add $- 2 x$ and $5 x$ .

$2 x^{2} + 3 x - 5 = - 6$

Step 1.2

Add $6$ to both sides of the equation.

$2 x^{2} + 3 x - 5 + 6 = 0$

Step 1.3

Add $- 5$ and $6$ .

$2 x^{2} + 3 x + 1 = 0$

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.

$a = 2$ , $b = 3$ , $c = 1$