Solve 42x^2-27x

$$42 { x }^{ 2 } -27x$$

Factor

$$3x\left(14x-9\right)$$

Solution Steps

Factor out 3.

$$3\left(14x^{2}-9x\right)$$

Consider 14x^{2}-9x. Factor out x.

$$x\left(14x-9\right)$$

Rewrite the complete factored expression.

$$3x\left(14x-9\right)$$

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.

$$42x^{2}-27x=0$$

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.

$$x=\frac{-\left(-27\right)±\sqrt{\left(-27\right)^{2}}}{2\times 42}$$

Take the square root of \left(-27\right)^{2}.

$$x=\frac{-\left(-27\right)±27}{2\times 42}$$

The opposite of -27 is 27.

$$x=\frac{27±27}{2\times 42}$$

Multiply 2 times 42.

$$x=\frac{27±27}{84}$$

Now solve the equation x=\frac{27±27}{84} when ± is plus. Add 27 to 27.

$$x=\frac{54}{84}$$

Reduce the fraction \frac{54}{84} to lowest terms by extracting and canceling out 6.

$$x=\frac{9}{14}$$

Now solve the equation x=\frac{27±27}{84} when ± is minus. Subtract 27 from 27.

$$x=\frac{0}{84}$$

Divide 0 by 84.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{9}{14} for x_{1} and 0 for x_{2}.

$$42x^{2}-27x=42\left(x-\frac{9}{14}\right)x$$

Subtract \frac{9}{14} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$42x^{2}-27x=42\times \frac{14x-9}{14}x$$

Cancel out 14, the greatest common factor in 42 and 14.

$$42x^{2}-27x=3\left(14x-9\right)x$$

Evaluate

$$3x\left(14x-9\right)$$