Solve by Factoring 5x^2+8x-69=0

$5 x^{2} + 8 x - 69 = 0$

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 $a \cdot c = 5 \cdot - 69 = - 345$ and whose sum is $b = 8$ .

Factor $8$ out of $8 x$ .

$5 x^{2} + 8 (x) - 69 = 0$

Rewrite $8$ as $- 15$ plus $23$

$5 x^{2} + (- 15 + 23) x - 69 = 0$

Apply the distributive property.

$5 x^{2} - 15 x + 23 x - 69 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} - 15 x) + 23 x - 69 = 0$

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

$5 x (x - 3) + 23 (x - 3) = 0$

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

$(x - 3) (5 x + 23) = 0$

Step 2

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

$x - 3 = 0$

$5 x + 23 = 0$

Step 3

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Step 4

Set $5 x + 23$ equal to $0$ and solve for $x$ .

Set $5 x + 23$ equal to $0$ .

$5 x + 23 = 0$

Solve $5 x + 23 = 0$ for $x$ .

Subtract $23$ from both sides of the equation.

$5 x = - 23$

Divide each term in $5 x = - 23$ by $5$ and simplify.

Divide each term in $5 x = - 23$ by $5$ .

$\frac{5 x}{5} = \frac{- 23}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 23}{5}$

Divide $x$ by $1$ .

$x = \frac{- 23}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{23}{5}$

Step 5

The final solution is all the values that make $(x - 3) (5 x + 23) = 0$ true.

$x = 3, - \frac{23}{5}$

Solve by Factoring 5x^2+8x-69=0

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