Solve 3x+2/6*x+2/3=0

$$\frac { 3 x + 2 } { 6 } \times \frac { x + 2 } { 3 } = 0$$

Solve for x

$$x=-2$$

$$x=-\frac{2}{3}\approx -0.666666667$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 6, the least common multiple of 6,3.

$$\left(3x+2\right)\times \frac{x+2}{3}=0$$

Express \left(3x+2\right)\times \frac{x+2}{3} as a single fraction.

$$\frac{\left(3x+2\right)\left(x+2\right)}{3}=0$$

Apply the distributive property by multiplying each term of 3x+2 by each term of x+2.

$$\frac{3x^{2}+6x+2x+4}{3}=0$$

Combine 6x and 2x to get 8x.

$$\frac{3x^{2}+8x+4}{3}=0$$

Divide each term of 3x^{2}+8x+4 by 3 to get x^{2}+\frac{8}{3}x+\frac{4}{3}.

$$x^{2}+\frac{8}{3}x+\frac{4}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, \frac{8}{3} for b, and \frac{4}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{8}{3}±\sqrt{\left(\frac{8}{3}\right)^{2}-4\times \frac{4}{3}}}{2}$$

Square \frac{8}{3} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\frac{8}{3}±\sqrt{\frac{64}{9}-4\times \frac{4}{3}}}{2}$$

Multiply -4 times \frac{4}{3}.

$$x=\frac{-\frac{8}{3}±\sqrt{\frac{64}{9}-\frac{16}{3}}}{2}$$

Add \frac{64}{9} to -\frac{16}{3} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{8}{3}±\sqrt{\frac{16}{9}}}{2}$$

Take the square root of \frac{16}{9}.

$$x=\frac{-\frac{8}{3}±\frac{4}{3}}{2}$$

Now solve the equation x=\frac{-\frac{8}{3}±\frac{4}{3}}{2} when ± is plus. Add -\frac{8}{3} to \frac{4}{3} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{4}{3}}{2}$$

Divide -\frac{4}{3} by 2.

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

Now solve the equation x=\frac{-\frac{8}{3}±\frac{4}{3}}{2} when ± is minus. Subtract \frac{4}{3} from -\frac{8}{3} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{4}{2}$$

Divide -4 by 2.

$$x=-2$$

The equation is now solved.

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

Steps for Completing the Square

Multiply both sides of the equation by 6, the least common multiple of 6,3.

$$\left(3x+2\right)\times \frac{x+2}{3}=0$$

Express \left(3x+2\right)\times \frac{x+2}{3} as a single fraction.

$$\frac{\left(3x+2\right)\left(x+2\right)}{3}=0$$

Apply the distributive property by multiplying each term of 3x+2 by each term of x+2.

$$\frac{3x^{2}+6x+2x+4}{3}=0$$

Combine 6x and 2x to get 8x.

$$\frac{3x^{2}+8x+4}{3}=0$$

Divide each term of 3x^{2}+8x+4 by 3 to get x^{2}+\frac{8}{3}x+\frac{4}{3}.

$$x^{2}+\frac{8}{3}x+\frac{4}{3}=0$$

Subtract \frac{4}{3} from both sides. Anything subtracted from zero gives its negation.

$$x^{2}+\frac{8}{3}x=-\frac{4}{3}$$

Divide \frac{8}{3}, the coefficient of the x term, by 2 to get \frac{4}{3}. Then add the square of \frac{4}{3} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{8}{3}x+\left(\frac{4}{3}\right)^{2}=-\frac{4}{3}+\left(\frac{4}{3}\right)^{2}$$

Square \frac{4}{3} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{8}{3}x+\frac{16}{9}=-\frac{4}{3}+\frac{16}{9}$$

Add -\frac{4}{3} to \frac{16}{9} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{8}{3}x+\frac{16}{9}=\frac{4}{9}$$

Factor x^{2}+\frac{8}{3}x+\frac{16}{9}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{4}{3}\right)^{2}=\frac{4}{9}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{4}{3}\right)^{2}}=\sqrt{\frac{4}{9}}$$

Simplify.

$$x+\frac{4}{3}=\frac{2}{3} x+\frac{4}{3}=-\frac{2}{3}$$

Subtract \frac{4}{3} from both sides of the equation.

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