Solve by Factoring 2x^2+13x-24=0

$2 x^{2} + 13 x - 24 = 0$

Step 1

Factor by grouping.

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 $a \cdot c = 2 \cdot - 24 = - 48$ and whose sum is $b = 13$ .

Factor $13$ out of $13 x$ .

$2 x^{2} + 13 (x) - 24 = 0$

Rewrite $13$ as $- 3$ plus $16$

$2 x^{2} + (- 3 + 16) x - 24 = 0$

Apply the distributive property.

$2 x^{2} - 3 x + 16 x - 24 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 3 x) + 16 x - 24 = 0$

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

$x (2 x - 3) + 8 (2 x - 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$(2 x - 3) (x + 8) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x - 3 = 0$

$x + 8 = 0$

Step 3

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 4

Set $x + 8$ equal to $0$ and solve for $x$ .

Set $x + 8$ equal to $0$ .

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 5

The final solution is all the values that make $(2 x - 3) (x + 8) = 0$ true.

$x = \frac{3}{2}, - 8$

Solve by Factoring 2x^2+13x-24=0

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