Solve by Factoring 5x^2+6x=-5x-2

$5 x^{2} + 6 x = - 5 x - 2$

Step 1

Move all the expressions to the left side of the equation.

Add $5 x$ to both sides of the equation.

$5 x^{2} + 6 x + 5 x = - 2$

Add $2$ to both sides of the equation.

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

Step 2

Add $6 x$ and $5 x$ .

$5 x^{2} + 11 x + 2 = 0$

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 $a \cdot c = 5 \cdot 2 = 10$ and whose sum is $b = 11$ .

Factor $11$ out of $11 x$ .

$5 x^{2} + 11 (x) + 2 = 0$

Rewrite $11$ as $1$ plus $10$

$5 x^{2} + (1 + 10) x + 2 = 0$

Apply the distributive property.

$5 x^{2} + 1 x + 10 x + 2 = 0$

Multiply $x$ by $1$ .

$5 x^{2} + x + 10 x + 2 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + x) + 10 x + 2 = 0$

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

$x (5 x + 1) + 2 (5 x + 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 x + 1$ .

$(5 x + 1) (x + 2) = 0$

Step 4

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

$5 x + 1 = 0$

$x + 2 = 0$

Step 5

Set $5 x + 1$ equal to $0$ and solve for $x$ .

Set $5 x + 1$ equal to $0$ .

$5 x + 1 = 0$

Solve $5 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$5 x = - 1$

Divide each term in $5 x = - 1$ by $5$ and simplify.

Divide each term in $5 x = - 1$ by $5$ .

$\frac{5 x}{5} = \frac{- 1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 1}{5}$

Divide $x$ by $1$ .

$x = \frac{- 1}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

Step 6

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 7

The final solution is all the values that make $(5 x + 1) (x + 2) = 0$ true.

$x = - \frac{1}{5}, - 2$

Solve by Factoring 5x^2+6x=-5x-2

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