Solve 36x^2-54x

$$36 { x }^{ 2 } -54x$$

Factor

$$18x\left(2x-3\right)$$

Solution Steps

Factor out 18.

$$18\left(2x^{2}-3x\right)$$

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

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

Rewrite the complete factored expression.

$$18x\left(2x-3\right)$$

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.

$$36x^{2}-54x=0$$

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.

$$x=\frac{-\left(-54\right)±\sqrt{\left(-54\right)^{2}}}{2\times 36}$$

Take the square root of \left(-54\right)^{2}.

$$x=\frac{-\left(-54\right)±54}{2\times 36}$$

The opposite of -54 is 54.

$$x=\frac{54±54}{2\times 36}$$

Multiply 2 times 36.

$$x=\frac{54±54}{72}$$

Now solve the equation x=\frac{54±54}{72} when ± is plus. Add 54 to 54.

$$x=\frac{108}{72}$$

Reduce the fraction \frac{108}{72} to lowest terms by extracting and canceling out 36.

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

Now solve the equation x=\frac{54±54}{72} when ± is minus. Subtract 54 from 54.

$$x=\frac{0}{72}$$

Divide 0 by 72.

$$x=0$$

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}.

$$36x^{2}-54x=36\left(x-\frac{3}{2}\right)x$$

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

$$36x^{2}-54x=36\times \frac{2x-3}{2}x$$

Cancel out 2, the greatest common factor in 36 and 2.

$$36x^{2}-54x=18\left(2x-3\right)x$$

Evaluate

$$18x\left(2x-3\right)$$