Solve 6b^2-10b

$$6 b ^ { 2 } - 10 b$$

Factor

$$2b\left(3b-5\right)$$

Solution Steps

Factor out 2.

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

Consider 3b^{2}-5b. Factor out b.

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

Rewrite the complete factored expression.

$$2b\left(3b-5\right)$$

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.

$$6b^{2}-10b=0$$

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.

$$b=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2\times 6}$$

Take the square root of \left(-10\right)^{2}.

$$b=\frac{-\left(-10\right)±10}{2\times 6}$$

The opposite of -10 is 10.

$$b=\frac{10±10}{2\times 6}$$

Multiply 2 times 6.

$$b=\frac{10±10}{12}$$

Now solve the equation b=\frac{10±10}{12} when ± is plus. Add 10 to 10.

$$b=\frac{20}{12}$$

Reduce the fraction \frac{20}{12} to lowest terms by extracting and canceling out 4.

$$b=\frac{5}{3}$$

Now solve the equation b=\frac{10±10}{12} when ± is minus. Subtract 10 from 10.

$$b=\frac{0}{12}$$

Divide 0 by 12.

$$b=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{5}{3} for x_{1} and 0 for x_{2}.

$$6b^{2}-10b=6\left(b-\frac{5}{3}\right)b$$

Subtract \frac{5}{3} from b by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$6b^{2}-10b=6\times \frac{3b-5}{3}b$$

Cancel out 3, the greatest common factor in 6 and 3.

$$6b^{2}-10b=2\left(3b-5\right)b$$

Evaluate

$$2b\left(3b-5\right)$$