Algebra Examples

$3 x^{2} - 9 = 26 x$

Step 1

Subtract $26 x$ from both sides of the equation.

$3 x^{2} - 9 - 26 x = 0$

Step 2

Factor by grouping.

Tap for more steps...

Step 2.1

Reorder terms.

$3 x^{2} - 26 x - 9 = 0$

Step 2.2

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 $a \cdot c = 3 \cdot - 9 = - 27$ and whose sum is $b = - 26$ .

Tap for more steps...

Step 2.2.1

Factor $- 26$ out of $- 26 x$ .

$3 x^{2} - 26 (x) - 9 = 0$

Step 2.2.2

Rewrite $- 26$ as $1$ plus $- 27$

$3 x^{2} + (1 - 27) x - 9 = 0$

Step 2.2.3

Apply the distributive property.

$3 x^{2} + 1 x - 27 x - 9 = 0$

Step 2.2.4

Multiply $x$ by $1$ .

$3 x^{2} + x - 27 x - 9 = 0$

Step 2.3

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.3.1

Group the first two terms and the last two terms.

$(3 x^{2} + x) - 27 x - 9 = 0$

Step 2.3.2

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

$x (3 x + 1) - 9 (3 x + 1) = 0$

Step 2.4

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$(3 x + 1) (x - 9) = 0$