Solve 16x^2-32x

$$16 x ^ { 2 } - 32 x$$

Factor

$$16x\left(x-2\right)$$

Solution Steps

Factor out 16.

$$16\left(x^{2}-2x\right)$$

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

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

Rewrite the complete factored expression.

$$16x\left(x-2\right)$$

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.

$$16x^{2}-32x=0$$

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.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}}}{2\times 16}$$

Take the square root of \left(-32\right)^{2}.

$$x=\frac{-\left(-32\right)±32}{2\times 16}$$

The opposite of -32 is 32.

$$x=\frac{32±32}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{32±32}{32}$$

Now solve the equation x=\frac{32±32}{32} when ± is plus. Add 32 to 32.

$$x=\frac{64}{32}$$

Divide 64 by 32.

$$x=2$$

Now solve the equation x=\frac{32±32}{32} when ± is minus. Subtract 32 from 32.

$$x=\frac{0}{32}$$

Divide 0 by 32.

$$x=0$$

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

$$16x^{2}-32x=16\left(x-2\right)x$$

Evaluate

$$16x\left(x-2\right)$$