Solve for x 2x-5=-3x^2

$2 x - 5 = - 3 x^{2}$

Step 1

Add $3 x^{2}$ to both sides of the equation.

$2 x - 5 + 3 x^{2} = 0$

Step 2

Factor by grouping.

Reorder terms.

$3 x^{2} + 2 x - 5 = 0$

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 $a \cdot c = 3 \cdot - 5 = - 15$ and whose sum is $b = 2$ .

Factor $2$ out of $2 x$ .

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

Rewrite $2$ as $- 3$ plus $5$

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

Apply the distributive property.

$3 x^{2} - 3 x + 5 x - 5 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$3 x (x - 1) + 5 (x - 1) = 0$

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

$(x - 1) (3 x + 5) = 0$

Step 3

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

$x - 1 = 0$

$3 x + 5 = 0$

Step 4

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 5

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

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

$3 x + 5 = 0$

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

Subtract $5$ from both sides of the equation.

$3 x = - 5$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 6

The final solution is all the values that make $(x - 1) (3 x + 5) = 0$ true.

$x = 1, - \frac{5}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 1, - \frac{5}{3}$

Decimal Form:

$x = 1, - 1.\overline{6}$

Mixed Number Form:

$x = 1, - 1 \frac{2}{3}$

Solve for x 2x-5=-3x^2

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