Solve 24x^2-28x

$$24 x ^ { 2 } - 28 x$$

Factor

$$4x\left(6x-7\right)$$

Solution Steps

Factor out 4.

$$4\left(6x^{2}-7x\right)$$

Consider 6x^{2}-7x. Factor out x.

$$x\left(6x-7\right)$$

Rewrite the complete factored expression.

$$4x\left(6x-7\right)$$

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.

$$24x^{2}-28x=0$$

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.

$$x=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}}}{2\times 24}$$

Take the square root of \left(-28\right)^{2}.

$$x=\frac{-\left(-28\right)±28}{2\times 24}$$

The opposite of -28 is 28.

$$x=\frac{28±28}{2\times 24}$$

Multiply 2 times 24.

$$x=\frac{28±28}{48}$$

Now solve the equation x=\frac{28±28}{48} when ± is plus. Add 28 to 28.

$$x=\frac{56}{48}$$

Reduce the fraction \frac{56}{48} to lowest terms by extracting and canceling out 8.

$$x=\frac{7}{6}$$

Now solve the equation x=\frac{28±28}{48} when ± is minus. Subtract 28 from 28.

$$x=\frac{0}{48}$$

Divide 0 by 48.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{7}{6} for x_{1} and 0 for x_{2}.

$$24x^{2}-28x=24\left(x-\frac{7}{6}\right)x$$

Subtract \frac{7}{6} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$24x^{2}-28x=24\times \frac{6x-7}{6}x$$

Cancel out 6, the greatest common factor in 24 and 6.

$$24x^{2}-28x=4\left(6x-7\right)x$$

Evaluate

$$4x\left(6x-7\right)$$