Solve 13m+15m^2

$$13 m + 15 m ^ { 2 }$$

Factor

$$m\left(15m+13\right)$$

Solution Steps

Factor out m.

$$m\left(13+15m\right)$$

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.

$$15m^{2}+13m=0$$

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.

$$m=\frac{-13±\sqrt{13^{2}}}{2\times 15}$$

Take the square root of 13^{2}.

$$m=\frac{-13±13}{2\times 15}$$

Multiply 2 times 15.

$$m=\frac{-13±13}{30}$$

Now solve the equation m=\frac{-13±13}{30} when ± is plus. Add -13 to 13.

$$m=\frac{0}{30}$$

Divide 0 by 30.

$$m=0$$

Now solve the equation m=\frac{-13±13}{30} when ± is minus. Subtract 13 from -13.

$$m=-\frac{26}{30}$$

Reduce the fraction \frac{-26}{30} to lowest terms by extracting and canceling out 2.

$$m=-\frac{13}{15}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -\frac{13}{15} for x_{2}.

$$15m^{2}+13m=15m\left(m-\left(-\frac{13}{15}\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$15m^{2}+13m=15m\left(m+\frac{13}{15}\right)$$

Add \frac{13}{15} to m by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$15m^{2}+13m=15m\times \frac{15m+13}{15}$$

Cancel out 15, the greatest common factor in 15 and 15.

$$15m^{2}+13m=m\left(15m+13\right)$$

Evaluate

$$m\left(15m+13\right)$$