Solve 72x-12x^2

$$72 x - 12 x ^ { 2 }$$

Factor

$$12x\left(6-x\right)$$

Solution Steps

Factor out 12.

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

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

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

Rewrite the complete factored expression.

$$12x\left(-x+6\right)$$

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.

$$-12x^{2}+72x=0$$

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.

$$x=\frac{-72±\sqrt{72^{2}}}{2\left(-12\right)}$$

Take the square root of 72^{2}.

$$x=\frac{-72±72}{2\left(-12\right)}$$

Multiply 2 times -12.

$$x=\frac{-72±72}{-24}$$

Now solve the equation x=\frac{-72±72}{-24} when ± is plus. Add -72 to 72.

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

Divide 0 by -24.

$$x=0$$

Now solve the equation x=\frac{-72±72}{-24} when ± is minus. Subtract 72 from -72.

$$x=-\frac{144}{-24}$$

Divide -144 by -24.

$$x=6$$

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 6 for x_{2}.

$$-12x^{2}+72x=-12x\left(x-6\right)$$

Evaluate

$$12x\left(6-x\right)$$