Solve 48w^2-36w

$$48 w ^ { 2 } - 36 w$$

Factor

$$12w\left(4w-3\right)$$

Solution Steps

Factor out 12.

$$12\left(4w^{2}-3w\right)$$

Consider 4w^{2}-3w. Factor out w.

$$w\left(4w-3\right)$$

Rewrite the complete factored expression.

$$12w\left(4w-3\right)$$

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.

$$48w^{2}-36w=0$$

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.

$$w=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}}}{2\times 48}$$

Take the square root of \left(-36\right)^{2}.

$$w=\frac{-\left(-36\right)±36}{2\times 48}$$

The opposite of -36 is 36.

$$w=\frac{36±36}{2\times 48}$$

Multiply 2 times 48.

$$w=\frac{36±36}{96}$$

Now solve the equation w=\frac{36±36}{96} when ± is plus. Add 36 to 36.

$$w=\frac{72}{96}$$

Reduce the fraction \frac{72}{96} to lowest terms by extracting and canceling out 24.

$$w=\frac{3}{4}$$

Now solve the equation w=\frac{36±36}{96} when ± is minus. Subtract 36 from 36.

$$w=\frac{0}{96}$$

Divide 0 by 96.

$$w=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{3}{4} for x_{1} and 0 for x_{2}.

$$48w^{2}-36w=48\left(w-\frac{3}{4}\right)w$$

Subtract \frac{3}{4} from w by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$48w^{2}-36w=48\times \frac{4w-3}{4}w$$

Cancel out 4, the greatest common factor in 48 and 4.

$$48w^{2}-36w=12\left(4w-3\right)w$$

Evaluate

$$12w\left(4w-3\right)$$