Solve 12b^2-15b

$$12 b ^ { 2 } - 15 b$$

Factor

$$3b\left(4b-5\right)$$

Solution Steps

Factor out 3.

$$3\left(4b^{2}-5b\right)$$

Consider 4b^{2}-5b. Factor out b.

$$b\left(4b-5\right)$$

Rewrite the complete factored expression.

$$3b\left(4b-5\right)$$

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.

$$12b^{2}-15b=0$$

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.

$$b=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}}}{2\times 12}$$

Take the square root of \left(-15\right)^{2}.

$$b=\frac{-\left(-15\right)±15}{2\times 12}$$

The opposite of -15 is 15.

$$b=\frac{15±15}{2\times 12}$$

Multiply 2 times 12.

$$b=\frac{15±15}{24}$$

Now solve the equation b=\frac{15±15}{24} when ± is plus. Add 15 to 15.

$$b=\frac{30}{24}$$

Reduce the fraction \frac{30}{24} to lowest terms by extracting and canceling out 6.

$$b=\frac{5}{4}$$

Now solve the equation b=\frac{15±15}{24} when ± is minus. Subtract 15 from 15.

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

Divide 0 by 24.

$$b=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{5}{4} for x_{1} and 0 for x_{2}.

$$12b^{2}-15b=12\left(b-\frac{5}{4}\right)b$$

Subtract \frac{5}{4} from b by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$12b^{2}-15b=12\times \frac{4b-5}{4}b$$

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

$$12b^{2}-15b=3\left(4b-5\right)b$$

Evaluate

$$3b\left(4b-5\right)$$