Solve -v+12v^2

$$- v + 12 v ^ { 2 }$$

Factor

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

Solution Steps

Factor out v.

$$v\left(-1+12v\right)$$

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.

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

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.

$$v=\frac{-\left(-1\right)±\sqrt{1}}{2\times 12}$$

Take the square root of 1.

$$v=\frac{-\left(-1\right)±1}{2\times 12}$$

The opposite of -1 is 1.

$$v=\frac{1±1}{2\times 12}$$

Multiply 2 times 12.

$$v=\frac{1±1}{24}$$

Now solve the equation v=\frac{1±1}{24} when ± is plus. Add 1 to 1.

$$v=\frac{2}{24}$$

Reduce the fraction \frac{2}{24} to lowest terms by extracting and canceling out 2.

$$v=\frac{1}{12}$$

Now solve the equation v=\frac{1±1}{24} when ± is minus. Subtract 1 from 1.

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

Divide 0 by 24.

$$v=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1}{12} for x_{1} and 0 for x_{2}.

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

Subtract \frac{1}{12} from v by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$12v^{2}-v=12\times \frac{12v-1}{12}v$$

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

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

Evaluate

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