Algebra Examples

$10 x^{2} + 15 x - 9 = 2 x^{2} + x - 14$

Step 1

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

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Step 1.1

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

$10 x^{2} + 15 x - 9 - 2 x^{2} = x - 14$

Step 1.2

Subtract $x$ from both sides of the equation.

$10 x^{2} + 15 x - 9 - 2 x^{2} - x = - 14$

Step 1.3

Add $14$ to both sides of the equation.

$10 x^{2} + 15 x - 9 - 2 x^{2} - x + 14 = 0$

Step 2

Simplify $10 x^{2} + 15 x - 9 - 2 x^{2} - x + 14$ .

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Step 2.1

Subtract $2 x^{2}$ from $10 x^{2}$ .

$8 x^{2} + 15 x - 9 - x + 14 = 0$

Step 2.2

Subtract $x$ from $15 x$ .

$8 x^{2} + 14 x - 9 + 14 = 0$

Step 2.3

Add $- 9$ and $14$ .

$8 x^{2} + 14 x + 5 = 0$

Step 3

Factor by grouping.

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Step 3.1

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 $a \cdot c = 8 \cdot 5 = 40$ and whose sum is $b = 14$ .

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Step 3.1.1

Factor $14$ out of $14 x$ .

$8 x^{2} + 14 (x) + 5 = 0$

Step 3.1.2

Rewrite $14$ as $4$ plus $10$

$8 x^{2} + (4 + 10) x + 5 = 0$

Step 3.1.3

Apply the distributive property.

$8 x^{2} + 4 x + 10 x + 5 = 0$

Step 3.2

Factor out the greatest common factor from each group.

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Step 3.2.1

Group the first two terms and the last two terms.

$(8 x^{2} + 4 x) + 10 x + 5 = 0$

Step 3.2.2

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

$4 x (2 x + 1) + 5 (2 x + 1) = 0$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$(2 x + 1) (4 x + 5) = 0$