Solve 21m^2+7m

$$21 m ^ { 2 } + 7 m$$

Factor

$$7m\left(3m+1\right)$$

Solution Steps

Factor out 7.

$$7\left(3m^{2}+m\right)$$

Consider 3m^{2}+m. Factor out m.

$$m\left(3m+1\right)$$

Rewrite the complete factored expression.

$$7m\left(3m+1\right)$$

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.

$$21m^{2}+7m=0$$

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.

$$m=\frac{-7±\sqrt{7^{2}}}{2\times 21}$$

Take the square root of 7^{2}.

$$m=\frac{-7±7}{2\times 21}$$

Multiply 2 times 21.

$$m=\frac{-7±7}{42}$$

Now solve the equation m=\frac{-7±7}{42} when ± is plus. Add -7 to 7.

$$m=\frac{0}{42}$$

Divide 0 by 42.

$$m=0$$

Now solve the equation m=\frac{-7±7}{42} when ± is minus. Subtract 7 from -7.

$$m=-\frac{14}{42}$$

Reduce the fraction \frac{-14}{42} to lowest terms by extracting and canceling out 14.

$$m=-\frac{1}{3}$$

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{1}{3} for x_{2}.

$$21m^{2}+7m=21m\left(m-\left(-\frac{1}{3}\right)\right)$$

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

$$21m^{2}+7m=21m\left(m+\frac{1}{3}\right)$$

Add \frac{1}{3} to m by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$21m^{2}+7m=21m\times \frac{3m+1}{3}$$

Cancel out 3, the greatest common factor in 21 and 3.

$$21m^{2}+7m=7m\left(3m+1\right)$$

Evaluate

$$7m\left(3m+1\right)$$