Solve -3x^2-2x=

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

Factor

$$-x\left(3x+2\right)$$

Solution Steps

Factor out x.

$$x\left(-3x-2\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

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

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

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

Take the square root of \left(-2\right)^{2}.

$$x=\frac{-\left(-2\right)±2}{2\left(-3\right)}$$

The opposite of -2 is 2.

$$x=\frac{2±2}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{2±2}{-6}$$

Now solve the equation x=\frac{2±2}{-6} when ± is plus. Add 2 to 2.

$$x=\frac{4}{-6}$$

Reduce the fraction \frac{4}{-6} to lowest terms by extracting and canceling out 2.

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

Now solve the equation x=\frac{2±2}{-6} when ± is minus. Subtract 2 from 2.

$$x=\frac{0}{-6}$$

Divide 0 by -6.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -\frac{2}{3} for x_{1} and 0 for x_{2}.

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

Simplify all the expressions of the form p-\left(-q\right) to p+q.

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

Add \frac{2}{3} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

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

Cancel out 3, the greatest common factor in -3 and -3.

$$-3x^{2}-2x=\left(-3x-2\right)x$$

Evaluate

$$-x\left(3x+2\right)$$