Solve 5x^2-6x

$$5 { x }^{ 2 } -6x$$

Factor

$$x\left(5x-6\right)$$

Solution Steps

Factor out x.

$$x\left(5x-6\right)$$

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.

$$5x^{2}-6x=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 5}$$

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

$$x=\frac{-\left(-6\right)±6}{2\times 5}$$

The opposite of -6 is 6.

$$x=\frac{6±6}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{6±6}{10}$$

Now solve the equation x=\frac{6±6}{10} when ± is plus. Add 6 to 6.

$$x=\frac{12}{10}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{6}{5}$$

Now solve the equation x=\frac{6±6}{10} when ± is minus. Subtract 6 from 6.

$$x=\frac{0}{10}$$

Divide 0 by 10.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{6}{5} for x_{1} and 0 for x_{2}.

$$5x^{2}-6x=5\left(x-\frac{6}{5}\right)x$$

Subtract \frac{6}{5} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$5x^{2}-6x=5\times \frac{5x-6}{5}x$$

Cancel out 5, the greatest common factor in 5 and 5.

$$5x^{2}-6x=\left(5x-6\right)x$$

Evaluate

$$x\left(5x-6\right)$$