Solve by Factoring 5x^2+18x+9=0

$5 x^{2} + 18 x + 9 = 0$

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 $a \cdot c = 5 \cdot 9 = 45$ and whose sum is $b = 18$ .

Factor $18$ out of $18 x$ .

$5 x^{2} + 18 (x) + 9 = 0$

Rewrite $18$ as $3$ plus $15$

$5 x^{2} + (3 + 15) x + 9 = 0$

Apply the distributive property.

$5 x^{2} + 3 x + 15 x + 9 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + 3 x) + 15 x + 9 = 0$

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

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

Factor the polynomial by factoring out the greatest common factor, $5 x + 3$ .

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

Step 2

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

$5 x + 3 = 0$

$x + 3 = 0$

Step 3

Set $5 x + 3$ equal to $0$ and solve for $x$ .

Set $5 x + 3$ equal to $0$ .

$5 x + 3 = 0$

Solve $5 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$5 x = - 3$

Divide each term in $5 x = - 3$ by $5$ and simplify.

Divide each term in $5 x = - 3$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 4

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 5

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

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

Solve by Factoring 5x^2+18x+9=0

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