Solve 3r-1*2r^2

$$3r-1 \cdot 2 { r }^{ 2 }$$

Factor

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

Solution Steps

Factor out r.

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

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.

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

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.

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

Take the square root of 3^{2}.

$$r=\frac{-3±3}{2\left(-2\right)}$$

Multiply 2 times -2.

$$r=\frac{-3±3}{-4}$$

Now solve the equation r=\frac{-3±3}{-4} when ± is plus. Add -3 to 3.

$$r=\frac{0}{-4}$$

Divide 0 by -4.

$$r=0$$

Now solve the equation r=\frac{-3±3}{-4} when ± is minus. Subtract 3 from -3.

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

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

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

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

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

Subtract \frac{3}{2} from r by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-2r^{2}+3r=-2r\times \frac{-2r+3}{-2}$$

Cancel out 2, the greatest common factor in -2 and -2.

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

Evaluate

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

Solution Steps

Multiply 1 and 2 to get 2.

$$3r-2r^{2}$$