Solve 7/12m/5000m=12(m-7/60.000m)

$$\frac { \frac { 7 } { 12 } m } { 5000 m } = 12 ( m - \frac { 7 } { 60.000 } m )$$

Solve for m

$$m=\frac{7}{636000}\approx 0.000011006$$

Steps Using Factoring

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15000m, the least common multiple of 5000m,60.

$$3\times \frac{7}{12}m=12\left(m-\frac{7}{60}m\right)\times 15000m$$

Multiply 3 and \frac{7}{12} to get \frac{7}{4}.

$$\frac{7}{4}m=12\left(m-\frac{7}{60}m\right)\times 15000m$$

Combine m and -\frac{7}{60}m to get \frac{53}{60}m.

$$\frac{7}{4}m=12\times \frac{53}{60}m\times 15000m$$

Multiply 12 and \frac{53}{60} to get \frac{53}{5}.

$$\frac{7}{4}m=\frac{53}{5}m\times 15000m$$

Multiply \frac{53}{5} and 15000 to get 159000.

$$\frac{7}{4}m=159000mm$$

Multiply m and m to get m^{2}.

$$\frac{7}{4}m=159000m^{2}$$

Subtract 159000m^{2} from both sides.

$$\frac{7}{4}m-159000m^{2}=0$$

Factor out m.

$$m\left(\frac{7}{4}-159000m\right)=0$$

To find equation solutions, solve m=0 and \frac{7}{4}-159000m=0.

$$m=0 m=\frac{7}{636000}$$

Variable m cannot be equal to 0.

$$m=\frac{7}{636000}$$

Steps Using the Quadratic Formula

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15000m, the least common multiple of 5000m,60.

$$3\times \frac{7}{12}m=12\left(m-\frac{7}{60}m\right)\times 15000m$$

Multiply 3 and \frac{7}{12} to get \frac{7}{4}.

$$\frac{7}{4}m=12\left(m-\frac{7}{60}m\right)\times 15000m$$

Combine m and -\frac{7}{60}m to get \frac{53}{60}m.

$$\frac{7}{4}m=12\times \frac{53}{60}m\times 15000m$$

Multiply 12 and \frac{53}{60} to get \frac{53}{5}.

$$\frac{7}{4}m=\frac{53}{5}m\times 15000m$$

Multiply \frac{53}{5} and 15000 to get 159000.

$$\frac{7}{4}m=159000mm$$

Multiply m and m to get m^{2}.

$$\frac{7}{4}m=159000m^{2}$$

Subtract 159000m^{2} from both sides.

$$\frac{7}{4}m-159000m^{2}=0$$

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.

$$-159000m^{2}+\frac{7}{4}m=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -159000 for a, \frac{7}{4} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\frac{7}{4}±\sqrt{\left(\frac{7}{4}\right)^{2}}}{2\left(-159000\right)}$$

Take the square root of \left(\frac{7}{4}\right)^{2}.

$$m=\frac{-\frac{7}{4}±\frac{7}{4}}{2\left(-159000\right)}$$

Multiply 2 times -159000.

$$m=\frac{-\frac{7}{4}±\frac{7}{4}}{-318000}$$

Now solve the equation m=\frac{-\frac{7}{4}±\frac{7}{4}}{-318000} when ± is plus. Add -\frac{7}{4} to \frac{7}{4} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$m=\frac{0}{-318000}$$

Divide 0 by -318000.

$$m=0$$

Now solve the equation m=\frac{-\frac{7}{4}±\frac{7}{4}}{-318000} when ± is minus. Subtract \frac{7}{4} from -\frac{7}{4} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$m=-\frac{\frac{7}{2}}{-318000}$$

Divide -\frac{7}{2} by -318000.

$$m=\frac{7}{636000}$$

The equation is now solved.

$$m=0 m=\frac{7}{636000}$$

Variable m cannot be equal to 0.

$$m=\frac{7}{636000}$$

Steps for Completing the Square

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15000m, the least common multiple of 5000m,60.

$$3\times \frac{7}{12}m=12\left(m-\frac{7}{60}m\right)\times 15000m$$

Multiply 3 and \frac{7}{12} to get \frac{7}{4}.

$$\frac{7}{4}m=12\left(m-\frac{7}{60}m\right)\times 15000m$$

Combine m and -\frac{7}{60}m to get \frac{53}{60}m.

$$\frac{7}{4}m=12\times \frac{53}{60}m\times 15000m$$

Multiply 12 and \frac{53}{60} to get \frac{53}{5}.

$$\frac{7}{4}m=\frac{53}{5}m\times 15000m$$

Multiply \frac{53}{5} and 15000 to get 159000.

$$\frac{7}{4}m=159000mm$$

Multiply m and m to get m^{2}.

$$\frac{7}{4}m=159000m^{2}$$

Subtract 159000m^{2} from both sides.

$$\frac{7}{4}m-159000m^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-159000m^{2}+\frac{7}{4}m=0$$

Divide both sides by -159000.

$$\frac{-159000m^{2}+\frac{7}{4}m}{-159000}=\frac{0}{-159000}$$

Dividing by -159000 undoes the multiplication by -159000.

$$m^{2}+\frac{\frac{7}{4}}{-159000}m=\frac{0}{-159000}$$

Divide \frac{7}{4} by -159000.

$$m^{2}-\frac{7}{636000}m=\frac{0}{-159000}$$

Divide 0 by -159000.

$$m^{2}-\frac{7}{636000}m=0$$

Divide -\frac{7}{636000}, the coefficient of the x term, by 2 to get -\frac{7}{1272000}. Then add the square of -\frac{7}{1272000} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-\frac{7}{636000}m+\left(-\frac{7}{1272000}\right)^{2}=\left(-\frac{7}{1272000}\right)^{2}$$

Square -\frac{7}{1272000} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-\frac{7}{636000}m+\frac{49}{1617984000000}=\frac{49}{1617984000000}$$

Factor m^{2}-\frac{7}{636000}m+\frac{49}{1617984000000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m-\frac{7}{1272000}\right)^{2}=\frac{49}{1617984000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{7}{1272000}\right)^{2}}=\sqrt{\frac{49}{1617984000000}}$$

Simplify.

$$m-\frac{7}{1272000}=\frac{7}{1272000} m-\frac{7}{1272000}=-\frac{7}{1272000}$$

Add \frac{7}{1272000} to both sides of the equation.

$$m=\frac{7}{636000} m=0$$

Variable m cannot be equal to 0.

$$m=\frac{7}{636000}$$