Solve -6x=15^2*8.854*10^-12*(80*10^-3+x)*20*10^-3

$$- 6 x = 15 ^ { 2 } \cdot 8.854 \cdot 10 ^ { - 12 } \cdot ( 80 \cdot 10 ^ { - 3 } + x ) \cdot 20 \cdot 10 ^ { - 3 }$$

Solve for x

$$x=-\frac{26562}{50000000000332025}\approx -5.3124 \cdot 10^{-13}$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add -12 and -3 to get -15.

$$-6x=15^{2}\times 8.854\times 10^{-15}\left(80\times 10^{-3}+x\right)\times 20$$

Calculate 15 to the power of 2 and get 225.

$$-6x=225\times 8.854\times 10^{-15}\left(80\times 10^{-3}+x\right)\times 20$$

Multiply 225 and 8.854 to get 1992.15.

$$-6x=1992.15\times 10^{-15}\left(80\times 10^{-3}+x\right)\times 20$$

Calculate 10 to the power of -15 and get \frac{1}{1000000000000000}.

$$-6x=1992.15\times \frac{1}{1000000000000000}\left(80\times 10^{-3}+x\right)\times 20$$

Multiply 1992.15 and \frac{1}{1000000000000000} to get \frac{39843}{20000000000000000}.

$$-6x=\frac{39843}{20000000000000000}\left(80\times 10^{-3}+x\right)\times 20$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$-6x=\frac{39843}{20000000000000000}\left(80\times \frac{1}{1000}+x\right)\times 20$$

Multiply 80 and \frac{1}{1000} to get \frac{2}{25}.

$$-6x=\frac{39843}{20000000000000000}\left(\frac{2}{25}+x\right)\times 20$$

Multiply \frac{39843}{20000000000000000} and 20 to get \frac{39843}{1000000000000000}.

$$-6x=\frac{39843}{1000000000000000}\left(\frac{2}{25}+x\right)$$

Use the distributive property to multiply \frac{39843}{1000000000000000} by \frac{2}{25}+x.

$$-6x=\frac{39843}{12500000000000000}+\frac{39843}{1000000000000000}x$$

Subtract \frac{39843}{1000000000000000}x from both sides.

$$-6x-\frac{39843}{1000000000000000}x=\frac{39843}{12500000000000000}$$

Combine -6x and -\frac{39843}{1000000000000000}x to get -\frac{6000000000039843}{1000000000000000}x.

$$-\frac{6000000000039843}{1000000000000000}x=\frac{39843}{12500000000000000}$$

Multiply both sides by -\frac{1000000000000000}{6000000000039843}, the reciprocal of -\frac{6000000000039843}{1000000000000000}.

$$x=\frac{39843}{12500000000000000}\left(-\frac{1000000000000000}{6000000000039843}\right)$$

Multiply \frac{39843}{12500000000000000} and -\frac{1000000000000000}{6000000000039843} to get -\frac{26562}{50000000000332025}.

$$x=-\frac{26562}{50000000000332025}$$