Solve 0.003=(0.002+z(0.002))*0.002

$$0.003 = ( 0.002 + z ( 0.002 ) ) * 0.002$$

Solve for z

$$z=749$$

Steps for Solving Linear Equation

Divide both sides by 0.002.

$$\frac{0.003}{0.002}=0.002+z\times 0.002$$

Expand \frac{0.003}{0.002} by multiplying both numerator and the denominator by 1000.

$$\frac{3}{2}=0.002+z\times 0.002$$

Swap sides so that all variable terms are on the left hand side.

$$0.002+z\times 0.002=\frac{3}{2}$$

Subtract 0.002 from both sides.

$$z\times 0.002=\frac{3}{2}-0.002$$

Convert decimal number 0.002 to fraction \frac{2}{1000}. Reduce the fraction \frac{2}{1000} to lowest terms by extracting and canceling out 2.

$$z\times 0.002=\frac{3}{2}-\frac{1}{500}$$

Least common multiple of 2 and 500 is 500. Convert \frac{3}{2} and \frac{1}{500} to fractions with denominator 500.

$$z\times 0.002=\frac{750}{500}-\frac{1}{500}$$

Since \frac{750}{500} and \frac{1}{500} have the same denominator, subtract them by subtracting their numerators.

$$z\times 0.002=\frac{750-1}{500}$$

Subtract 1 from 750 to get 749.

$$z\times 0.002=\frac{749}{500}$$

Divide both sides by 0.002.

$$z=\frac{\frac{749}{500}}{0.002}$$

Express \frac{\frac{749}{500}}{0.002} as a single fraction.

$$z=\frac{749}{500\times 0.002}$$

Multiply 500 and 0.002 to get 1.

$$z=\frac{749}{1}$$

Divide 749 by 1 to get 749.

$$z=749$$