Solve -f-6*0.6=1/2*0.6*10*0.3-1/2*0.6*16

$$-f-6 \cdot 0.6 = \frac{ 1 }{ 2 } \times 0.6 \cdot 10 \cdot 0.3- \frac{ 1 }{ 2 } \times 0.6 \cdot 16$$

Solve for f

$$f=0.3$$

Steps for Solving Linear Equation

Multiply 6 and 0.6 to get 3.6.

$$-f-3.6=\frac{1}{2}\times 0.6\times 10\times 0.3-\frac{1}{2}\times 0.6\times 16$$

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$-f-3.6=\frac{1}{2}\times \frac{3}{5}\times 10\times 0.3-\frac{1}{2}\times 0.6\times 16$$

Multiply \frac{1}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$-f-3.6=\frac{1\times 3}{2\times 5}\times 10\times 0.3-\frac{1}{2}\times 0.6\times 16$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 5}.

$$-f-3.6=\frac{3}{10}\times 10\times 0.3-\frac{1}{2}\times 0.6\times 16$$

Cancel out 10 and 10.

$$-f-3.6=3\times 0.3-\frac{1}{2}\times 0.6\times 16$$

Multiply 3 and 0.3 to get 0.9.

$$-f-3.6=0.9-\frac{1}{2}\times 0.6\times 16$$

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$-f-3.6=0.9-\frac{1}{2}\times \frac{3}{5}\times 16$$

Multiply \frac{1}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$-f-3.6=0.9-\frac{1\times 3}{2\times 5}\times 16$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 5}.

$$-f-3.6=0.9-\frac{3}{10}\times 16$$

Express \frac{3}{10}\times 16 as a single fraction.

$$-f-3.6=0.9-\frac{3\times 16}{10}$$

Multiply 3 and 16 to get 48.

$$-f-3.6=0.9-\frac{48}{10}$$

Reduce the fraction \frac{48}{10} to lowest terms by extracting and canceling out 2.

$$-f-3.6=0.9-\frac{24}{5}$$

Convert decimal number 0.9 to fraction \frac{9}{10}.

$$-f-3.6=\frac{9}{10}-\frac{24}{5}$$

Least common multiple of 10 and 5 is 10. Convert \frac{9}{10} and \frac{24}{5} to fractions with denominator 10.

$$-f-3.6=\frac{9}{10}-\frac{48}{10}$$

Since \frac{9}{10} and \frac{48}{10} have the same denominator, subtract them by subtracting their numerators.

$$-f-3.6=\frac{9-48}{10}$$

Subtract 48 from 9 to get -39.

$$-f-3.6=-\frac{39}{10}$$

Add 3.6 to both sides.

$$-f=-\frac{39}{10}+3.6$$

Convert decimal number 3.6 to fraction \frac{36}{10}. Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$-f=-\frac{39}{10}+\frac{18}{5}$$

Least common multiple of 10 and 5 is 10. Convert -\frac{39}{10} and \frac{18}{5} to fractions with denominator 10.

$$-f=-\frac{39}{10}+\frac{36}{10}$$

Since -\frac{39}{10} and \frac{36}{10} have the same denominator, add them by adding their numerators.

$$-f=\frac{-39+36}{10}$$

Add -39 and 36 to get -3.

$$-f=-\frac{3}{10}$$

Multiply both sides by -1.

$$f=\frac{3}{10}$$