Solve by Factoring 5x^2+22x+8=(5x+2)

$5 x^{2} + 22 x + 8 = (5 x + 2)$

Step 1

Subtract $(5 x + 2)$ from both sides of the equation.

$5 x^{2} + 22 x + 8 - (5 x + 2) = 0$

Step 2

Simplify $5 x^{2} + 22 x + 8 - (5 x + 2)$ .

Simplify each term.

Apply the distributive property.

$5 x^{2} + 22 x + 8 - (5 x) - 1 \cdot 2 = 0$

Multiply $5$ by $- 1$ .

$5 x^{2} + 22 x + 8 - 5 x - 1 \cdot 2 = 0$

Multiply $- 1$ by $2$ .

$5 x^{2} + 22 x + 8 - 5 x - 2 = 0$

Subtract $5 x$ from $22 x$ .

$5 x^{2} + 17 x + 8 - 2 = 0$

Subtract $2$ from $8$ .

$5 x^{2} + 17 x + 6 = 0$

Step 3

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 $a \cdot c = 5 \cdot 6 = 30$ and whose sum is $b = 17$ .

Factor $17$ out of $17 x$ .

$5 x^{2} + 17 (x) + 6 = 0$

Rewrite $17$ as $2$ plus $15$

$5 x^{2} + (2 + 15) x + 6 = 0$

Apply the distributive property.

$5 x^{2} + 2 x + 15 x + 6 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + 2 x) + 15 x + 6 = 0$

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

$x (5 x + 2) + 3 (5 x + 2) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 x + 2$ .

$(5 x + 2) (x + 3) = 0$

Step 4

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

$5 x + 2 = 0$

$x + 3 = 0$

Step 5

Set $5 x + 2$ equal to $0$ and solve for $x$ .

Set $5 x + 2$ equal to $0$ .

$5 x + 2 = 0$

Solve $5 x + 2 = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$5 x = - 2$

Divide each term in $5 x = - 2$ by $5$ and simplify.

Divide each term in $5 x = - 2$ by $5$ .

$\frac{5 x}{5} = \frac{- 2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 2}{5}$

Divide $x$ by $1$ .

$x = \frac{- 2}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{5}$

Step 6

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 7

The final solution is all the values that make $(5 x + 2) (x + 3) = 0$ true.

$x = - \frac{2}{5}, - 3$

Solve by Factoring 5x^2+22x+8=(5x+2)

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