Solve 12x^2-16x

$$12 x ^ { 2 } - 16 x$$

Factor

$$4x\left(3x-4\right)$$

Solution Steps

Factor out 4.

$$4\left(3x^{2}-4x\right)$$

Consider 3x^{2}-4x. Factor out x.

$$x\left(3x-4\right)$$

Rewrite the complete factored expression.

$$4x\left(3x-4\right)$$

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.

$$12x^{2}-16x=0$$

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.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}}}{2\times 12}$$

Take the square root of \left(-16\right)^{2}.

$$x=\frac{-\left(-16\right)±16}{2\times 12}$$

The opposite of -16 is 16.

$$x=\frac{16±16}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{16±16}{24}$$

Now solve the equation x=\frac{16±16}{24} when ± is plus. Add 16 to 16.

$$x=\frac{32}{24}$$

Reduce the fraction \frac{32}{24} to lowest terms by extracting and canceling out 8.

$$x=\frac{4}{3}$$

Now solve the equation x=\frac{16±16}{24} when ± is minus. Subtract 16 from 16.

$$x=\frac{0}{24}$$

Divide 0 by 24.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{4}{3} for x_{1} and 0 for x_{2}.

$$12x^{2}-16x=12\left(x-\frac{4}{3}\right)x$$

Subtract \frac{4}{3} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$12x^{2}-16x=12\times \frac{3x-4}{3}x$$

Cancel out 3, the greatest common factor in 12 and 3.

$$12x^{2}-16x=4\left(3x-4\right)x$$

Evaluate

$$4x\left(3x-4\right)$$