Solve 4y^2-6y

$$4 y ^ { 2 } - 6 y$$

Factor

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

Solution Steps

Factor out 2.

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

Consider 2y^{2}-3y. Factor out y.

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

Rewrite the complete factored expression.

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

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.

$$4y^{2}-6y=0$$

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.

$$y=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 4}$$

Take the square root of \left(-6\right)^{2}.

$$y=\frac{-\left(-6\right)±6}{2\times 4}$$

The opposite of -6 is 6.

$$y=\frac{6±6}{2\times 4}$$

Multiply 2 times 4.

$$y=\frac{6±6}{8}$$

Now solve the equation y=\frac{6±6}{8} when ± is plus. Add 6 to 6.

$$y=\frac{12}{8}$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

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

Now solve the equation y=\frac{6±6}{8} when ± is minus. Subtract 6 from 6.

$$y=\frac{0}{8}$$

Divide 0 by 8.

$$y=0$$

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

$$4y^{2}-6y=4\left(y-\frac{3}{2}\right)y$$

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

$$4y^{2}-6y=4\times \frac{2y-3}{2}y$$

Cancel out 2, the greatest common factor in 4 and 2.

$$4y^{2}-6y=2\left(2y-3\right)y$$

Evaluate

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