Solve for x 4x-2=-3x^2+3x

$4 x - 2 = - 3 x^{2} + 3 x$

Step 1

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

$- 3 x^{2} + 3 x = 4 x - 2$

Step 2

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

Subtract $4 x$ from both sides of the equation.

$- 3 x^{2} + 3 x - 4 x = - 2$

Subtract $4 x$ from $3 x$ .

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

Step 3

Add $2$ to both sides of the equation.

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

Step 4

Factor the left side of the equation.

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

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

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

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

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

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

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

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

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

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

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

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 $a \cdot c = 3 \cdot - 2 = - 6$ and whose sum is $b = 1$ .

Multiply by $1$ .

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

Rewrite $1$ as $- 2$ plus $3$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$- (x (3 x - 2) + 1 (3 x - 2)) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 x - 2$ .

$- ((3 x - 2) (x + 1)) = 0$

Remove unnecessary parentheses.

$- (3 x - 2) (x + 1) = 0$

Step 5

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

$3 x - 2 = 0$

$x + 1 = 0$

Step 6

Set $3 x - 2$ equal to $0$ and solve for $x$ .

Set $3 x - 2$ equal to $0$ .

$3 x - 2 = 0$

Solve $3 x - 2 = 0$ for $x$ .

Add $2$ to both sides of the equation.

$3 x = 2$

Divide each term in $3 x = 2$ by $3$ and simplify.

Divide each term in $3 x = 2$ by $3$ .

$\frac{3 x}{3} = \frac{2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{2}{3}$

Divide $x$ by $1$ .

$x = \frac{2}{3}$

Step 7

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 8

The final solution is all the values that make $- (3 x - 2) (x + 1) = 0$ true.

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

Step 9

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{6}, - 1$

Solve for x 4x-2=-3x^2+3x

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