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

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

Solve for f

$$f = -\frac{13}{12} = -1\frac{1}{12} \approx -1.083333333$$

Steps for Solving Linear Equation

Multiply -6 and 0.6 to get -3.6.

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

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.

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

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

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

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

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

Cancel out 10 and 10.

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

Multiply 3 and 0.3 to get 0.9.

$$\left(-f\right)\left(-3.6\right)=0.9-\frac{1}{2}\times 0.6\times 16$$

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.

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

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

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

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

$$\left(-f\right)\left(-3.6\right)=0.9-\frac{3}{10}\times 16$$

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

$$\left(-f\right)\left(-3.6\right)=0.9-\frac{3\times 16}{10}$$

Multiply 3 and 16 to get 48.

$$\left(-f\right)\left(-3.6\right)=0.9-\frac{48}{10}$$

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

$$\left(-f\right)\left(-3.6\right)=0.9-\frac{24}{5}$$

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

$$\left(-f\right)\left(-3.6\right)=\frac{9}{10}-\frac{24}{5}$$

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

$$\left(-f\right)\left(-3.6\right)=\frac{9}{10}-\frac{48}{10}$$

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

$$\left(-f\right)\left(-3.6\right)=\frac{9-48}{10}$$

Subtract 48 from 9 to get -39.

$$\left(-f\right)\left(-3.6\right)=-\frac{39}{10}$$

Divide both sides by -3.6.

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

Express \frac{-\frac{39}{10}}{-3.6} as a single fraction.

$$-f=\frac{-39}{10\left(-3.6\right)}$$

Multiply 10 and -3.6 to get -36.

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

Reduce the fraction \frac{-39}{-36} to lowest terms by extracting and canceling out -3.

$$-f=\frac{13}{12}$$

Multiply both sides by -1.

$$f=-\frac{13}{12}$$