Solve by Factoring 4x^2+23x-72=0

$4 x^{2} + 23 x - 72 = 0$

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 $a \cdot c = 4 \cdot - 72 = - 288$ and whose sum is $b = 23$ .

Factor $23$ out of $23 x$ .

$4 x^{2} + 23 (x) - 72 = 0$

Rewrite $23$ as $- 9$ plus $32$

$4 x^{2} + (- 9 + 32) x - 72 = 0$

Apply the distributive property.

$4 x^{2} - 9 x + 32 x - 72 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 9 x) + 32 x - 72 = 0$

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

$x (4 x - 9) + 8 (4 x - 9) = 0$

Factor the polynomial by factoring out the greatest common factor, $4 x - 9$ .

$(4 x - 9) (x + 8) = 0$

Step 2

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

$4 x - 9 = 0$

$x + 8 = 0$

Step 3

Set $4 x - 9$ equal to $0$ and solve for $x$ .

Set $4 x - 9$ equal to $0$ .

$4 x - 9 = 0$

Solve $4 x - 9 = 0$ for $x$ .

Add $9$ to both sides of the equation.

$4 x = 9$

Divide each term in $4 x = 9$ by $4$ and simplify.

Divide each term in $4 x = 9$ by $4$ .

$\frac{4 x}{4} = \frac{9}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{9}{4}$

Divide $x$ by $1$ .

$x = \frac{9}{4}$

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 $(4 x - 9) (x + 8) = 0$ true.

$x = \frac{9}{4}, - 8$

Solve by Factoring 4x^2+23x-72=0

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