Solve 12x-6x^2

$$12 x - 6 x ^ { 2 }$$

Factor

$$6x\left(2-x\right)$$

Solution Steps

Factor out 6.

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

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

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

Rewrite the complete factored expression.

$$6x\left(-x+2\right)$$

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.

$$-6x^{2}+12x=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}}}{2\left(-6\right)}$$

Take the square root of 12^{2}.

$$x=\frac{-12±12}{2\left(-6\right)}$$

Multiply 2 times -6.

$$x=\frac{-12±12}{-12}$$

Now solve the equation x=\frac{-12±12}{-12} when ± is plus. Add -12 to 12.

$$x=\frac{0}{-12}$$

Divide 0 by -12.

$$x=0$$

Now solve the equation x=\frac{-12±12}{-12} when ± is minus. Subtract 12 from -12.

$$x=-\frac{24}{-12}$$

Divide -24 by -12.

$$x=2$$

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

$$-6x^{2}+12x=-6x\left(x-2\right)$$

Evaluate

$$6x\left(2-x\right)$$