Solve 28m^2+18m

$$28 m ^ { 2 } + 18 m$$

Factor

$$2m\left(14m+9\right)$$

Solution Steps

Factor out 2.

$$2\left(14m^{2}+9m\right)$$

Consider 14m^{2}+9m. Factor out m.

$$m\left(14m+9\right)$$

Rewrite the complete factored expression.

$$2m\left(14m+9\right)$$

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.

$$28m^{2}+18m=0$$

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.

$$m=\frac{-18±\sqrt{18^{2}}}{2\times 28}$$

Take the square root of 18^{2}.

$$m=\frac{-18±18}{2\times 28}$$

Multiply 2 times 28.

$$m=\frac{-18±18}{56}$$

Now solve the equation m=\frac{-18±18}{56} when ± is plus. Add -18 to 18.

$$m=\frac{0}{56}$$

Divide 0 by 56.

$$m=0$$

Now solve the equation m=\frac{-18±18}{56} when ± is minus. Subtract 18 from -18.

$$m=-\frac{36}{56}$$

Reduce the fraction \frac{-36}{56} to lowest terms by extracting and canceling out 4.

$$m=-\frac{9}{14}$$

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{9}{14} for x_{2}.

$$28m^{2}+18m=28m\left(m-\left(-\frac{9}{14}\right)\right)$$

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

$$28m^{2}+18m=28m\left(m+\frac{9}{14}\right)$$

Add \frac{9}{14} to m by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$28m^{2}+18m=28m\times \frac{14m+9}{14}$$

Cancel out 14, the greatest common factor in 28 and 14.

$$28m^{2}+18m=2m\left(14m+9\right)$$

Evaluate

$$2m\left(14m+9\right)$$