Solve 6*10^{3}*10*(12/0.6*10^4*4*10^-2-h)=(h*4*10^-2*6*10^3)*10+5.4*10/0.2*0.3

$$6 \times 10 ^ { 3 } \times 10 \times ( \frac { 12 } { 0.6 \times 10 ^ { 4 } \times 4 \times 10 ^ { - 2 } } - h ) = \frac { ( h \times 4 \times 10 ^ { - 2 } \times 6 \times 10 ^ { 3 } ) \times 10 + 5.4 \times 10 } { 0.2 \times 0.3 }$$

Solve for h

$$h=0.021$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 4 and -2 to get 2.

$$6\times 10^{3}\times 10\left(\frac{12}{0.6\times 10^{2}\times 4}-h\right)=\frac{h\times 4\times 10^{-2}\times 6\times 10^{3}\times 10+5.4\times 10}{0.2\times 0.3}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$6\times 10^{4}\left(\frac{12}{0.6\times 10^{2}\times 4}-h\right)=\frac{h\times 4\times 10^{-2}\times 6\times 10^{3}\times 10+5.4\times 10}{0.2\times 0.3}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$6\times 10^{4}\left(\frac{12}{0.6\times 10^{2}\times 4}-h\right)=\frac{h\times 4\times 10^{1}\times 6\times 10+5.4\times 10}{0.2\times 0.3}$$

To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.

$$6\times 10^{4}\left(\frac{12}{0.6\times 10^{2}\times 4}-h\right)=\frac{h\times 4\times 10^{2}\times 6+5.4\times 10}{0.2\times 0.3}$$

Calculate 10 to the power of 4 and get 10000.

$$6\times 10000\left(\frac{12}{0.6\times 10^{2}\times 4}-h\right)=\frac{h\times 4\times 10^{2}\times 6+5.4\times 10}{0.2\times 0.3}$$

Multiply 6 and 10000 to get 60000.

$$60000\left(\frac{12}{0.6\times 10^{2}\times 4}-h\right)=\frac{h\times 4\times 10^{2}\times 6+5.4\times 10}{0.2\times 0.3}$$

Calculate 10 to the power of 2 and get 100.

$$60000\left(\frac{12}{0.6\times 100\times 4}-h\right)=\frac{h\times 4\times 10^{2}\times 6+5.4\times 10}{0.2\times 0.3}$$

Multiply 0.6 and 100 to get 60.

$$60000\left(\frac{12}{60\times 4}-h\right)=\frac{h\times 4\times 10^{2}\times 6+5.4\times 10}{0.2\times 0.3}$$

Multiply 60 and 4 to get 240.

$$60000\left(\frac{12}{240}-h\right)=\frac{h\times 4\times 10^{2}\times 6+5.4\times 10}{0.2\times 0.3}$$

Reduce the fraction \frac{12}{240} to lowest terms by extracting and canceling out 12.

$$60000\left(\frac{1}{20}-h\right)=\frac{h\times 4\times 10^{2}\times 6+5.4\times 10}{0.2\times 0.3}$$

Use the distributive property to multiply 60000 by \frac{1}{20}-h.

$$3000-60000h=\frac{h\times 4\times 10^{2}\times 6+5.4\times 10}{0.2\times 0.3}$$

Calculate 10 to the power of 2 and get 100.

$$3000-60000h=\frac{h\times 4\times 100\times 6+5.4\times 10}{0.2\times 0.3}$$

Multiply 4 and 100 to get 400.

$$3000-60000h=\frac{h\times 400\times 6+5.4\times 10}{0.2\times 0.3}$$

Multiply 400 and 6 to get 2400.

$$3000-60000h=\frac{h\times 2400+5.4\times 10}{0.2\times 0.3}$$

Multiply 5.4 and 10 to get 54.

$$3000-60000h=\frac{h\times 2400+54}{0.2\times 0.3}$$

Multiply 0.2 and 0.3 to get 0.06.

$$3000-60000h=\frac{h\times 2400+54}{0.06}$$

Divide each term of h\times 2400+54 by 0.06 to get \frac{h\times 2400}{0.06}+\frac{54}{0.06}.

$$3000-60000h=\frac{h\times 2400}{0.06}+\frac{54}{0.06}$$

Divide h\times 2400 by 0.06 to get h\times 40000.

$$3000-60000h=h\times 40000+\frac{54}{0.06}$$

Expand \frac{54}{0.06} by multiplying both numerator and the denominator by 100.

$$3000-60000h=h\times 40000+\frac{5400}{6}$$

Divide 5400 by 6 to get 900.

$$3000-60000h=h\times 40000+900$$

Subtract h\times 40000 from both sides.

$$3000-60000h-h\times 40000=900$$

Combine -60000h and -h\times 40000 to get -100000h.

$$3000-100000h=900$$

Subtract 3000 from both sides.

$$-100000h=900-3000$$

Subtract 3000 from 900 to get -2100.

$$-100000h=-2100$$

Divide both sides by -100000.

$$h=\frac{-2100}{-100000}$$

Reduce the fraction \frac{-2100}{-100000} to lowest terms by extracting and canceling out -100.

$$h=\frac{21}{1000}$$