Find the Roots (Zeros) -5x-2=-2x^2-2x

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

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Move all terms containing $x$ to the left side of the equation.

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

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

Add $- 2 x$ and $5 x$ .

$- 2 x^{2} + 3 x = - 2$

Add $2$ to both sides of the equation.

$- 2 x^{2} + 3 x + 2 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $- 2 x^{2} + 3 x + 2$ .

Factor $- 1$ out of $- 2 x^{2}$ .

$- (2 x^{2}) + 3 x + 2 = 0$

Factor $- 1$ out of $3 x$ .

$- (2 x^{2}) - (- 3 x) + 2 = 0$

Rewrite $2$ as $- 1 (- 2)$ .

$- (2 x^{2}) - (- 3 x) - 1 \cdot - 2 = 0$

Factor $- 1$ out of $- (2 x^{2}) - (- 3 x)$ .

$- (2 x^{2} - 3 x) - 1 \cdot - 2 = 0$

Factor $- 1$ out of $- (2 x^{2} - 3 x) - 1 (- 2)$ .

$- (2 x^{2} - 3 x - 2) = 0$

Factor.

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 $a \cdot c = 2 \cdot - 2 = - 4$ and whose sum is $b = - 3$ .

Factor $- 3$ out of $- 3 x$ .

$- (2 x^{2} - 3 x - 2) = 0$

Rewrite $- 3$ as $1$ plus $- 4$

$- (2 x^{2} + (1 - 4) x - 2) = 0$

Apply the distributive property.

$- (2 x^{2} + 1 x - 4 x - 2) = 0$

Multiply $x$ by $1$ .

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

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

Remove unnecessary parentheses.

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

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

$2 x + 1 = 0$

$x - 2 = 0$

Set $2 x + 1$ equal to $0$ and solve for $x$ .

Set $2 x + 1$ equal to $0$ .

$2 x + 1 = 0$

Solve $2 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

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

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

Find the Roots (Zeros) -5x-2=-2x^2-2x

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