Finite Math Examples

$2 x^{2} + x = 15$

Step 1

Subtract $15$ from both sides of the equation.

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

Step 2

Factor by grouping.

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Step 2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot - 15 = - 30$ and whose sum is $b = 1$ .

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Step 2.1.1

Multiply by $1$ .

$2 x^{2} + 1 x - 15 = 0$

Step 2.1.2

Rewrite $1$ as $- 5$ plus $6$

$2 x^{2} + (- 5 + 6) x - 15 = 0$

Step 2.1.3

Apply the distributive property.

$2 x^{2} - 5 x + 6 x - 15 = 0$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$(2 x^{2} - 5 x) + 6 x - 15 = 0$

Step 2.2.2

Factor out the greatest common factor (GCF) from each group.

$x (2 x - 5) + 3 (2 x - 5) = 0$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $2 x - 5$ .

$(2 x - 5) (x + 3) = 0$