Solve 12t^2-3t=

$$12 t ^ { 2 } - 3 t =$$

Factor

$$3t\left(4t-1\right)$$

Solution Steps

Factor out 3.

$$3\left(4t^{2}-t\right)$$

Consider 4t^{2}-t. Factor out t.

$$t\left(4t-1\right)$$

Rewrite the complete factored expression.

$$3t\left(4t-1\right)$$

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.

$$12t^{2}-3t=0$$

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.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 12}$$

Take the square root of \left(-3\right)^{2}.

$$t=\frac{-\left(-3\right)±3}{2\times 12}$$

The opposite of -3 is 3.

$$t=\frac{3±3}{2\times 12}$$

Multiply 2 times 12.

$$t=\frac{3±3}{24}$$

Now solve the equation t=\frac{3±3}{24} when ± is plus. Add 3 to 3.

$$t=\frac{6}{24}$$

Reduce the fraction \frac{6}{24} to lowest terms by extracting and canceling out 6.

$$t=\frac{1}{4}$$

Now solve the equation t=\frac{3±3}{24} when ± is minus. Subtract 3 from 3.

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

Divide 0 by 24.

$$t=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1}{4} for x_{1} and 0 for x_{2}.

$$12t^{2}-3t=12\left(t-\frac{1}{4}\right)t$$

Subtract \frac{1}{4} from t by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$12t^{2}-3t=12\times \frac{4t-1}{4}t$$

Cancel out 4, the greatest common factor in 12 and 4.

$$12t^{2}-3t=3\left(4t-1\right)t$$

Evaluate

$$3t\left(4t-1\right)$$