Solve 12x^2-12x

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

Factor

$$12x\left(x-1\right)$$

Solution Steps

Factor out 12.

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

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

$$x\left(x-1\right)$$

Rewrite the complete factored expression.

$$12x\left(x-1\right)$$

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.

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

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.

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

Take the square root of \left(-12\right)^{2}.

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

The opposite of -12 is 12.

$$x=\frac{12±12}{2\times 12}$$

Multiply 2 times 12.

$$x=\frac{12±12}{24}$$

Now solve the equation x=\frac{12±12}{24} when ± is plus. Add 12 to 12.

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

Divide 24 by 24.

$$x=1$$

Now solve the equation x=\frac{12±12}{24} when ± is minus. Subtract 12 from 12.

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

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 1 for x_{1} and 0 for x_{2}.

$$12x^{2}-12x=12\left(x-1\right)x$$

Evaluate

$$12x\left(x-1\right)$$