Solve 1.8-8x/1.2^6-1.3-3x/2-5x-0.4/0.3frac{3{10}}=0

$$\frac { 1.8 - 8 x } { 1.2 ^ { 6 } } - \frac { 1.3 - 3 x } { 2 } - \frac { 5 x - 0.4 } { 0.3 \frac { 3 } { 10 } } = 0$$

Solve for x

$$x=\frac{144513}{2219080}\approx 0.065122934$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$\frac{15625}{23328}\left(1.8-8x\right)-\left(1.3-3x\right)-\frac{10}{3}\left(5x-0.4\right)=0$$

Use the distributive property to multiply \frac{15625}{23328} by 1.8-8x.

$$\frac{3125}{2592}-\frac{15625}{2916}x-\left(1.3-3x\right)-\frac{10}{3}\left(5x-0.4\right)=0$$

To find the opposite of 1.3-3x, find the opposite of each term.

$$\frac{3125}{2592}-\frac{15625}{2916}x-1.3-\left(-3x\right)-\frac{10}{3}\left(5x-0.4\right)=0$$

The opposite of -3x is 3x.

$$\frac{3125}{2592}-\frac{15625}{2916}x-1.3+3x-\frac{10}{3}\left(5x-0.4\right)=0$$

Subtract 1.3 from \frac{3125}{2592} to get -\frac{1223}{12960}.

$$-\frac{1223}{12960}-\frac{15625}{2916}x+3x-\frac{10}{3}\left(5x-0.4\right)=0$$

Combine -\frac{15625}{2916}x and 3x to get -\frac{6877}{2916}x.

$$-\frac{1223}{12960}-\frac{6877}{2916}x-\frac{10}{3}\left(5x-0.4\right)=0$$

Use the distributive property to multiply -\frac{10}{3} by 5x-0.4.

$$-\frac{1223}{12960}-\frac{6877}{2916}x-\frac{10}{3}\times 5x-\frac{10}{3}\left(-0.4\right)=0$$

Express -\frac{10}{3}\times 5 as a single fraction.

$$-\frac{1223}{12960}-\frac{6877}{2916}x+\frac{-10\times 5}{3}x-\frac{10}{3}\left(-0.4\right)=0$$

Multiply -10 and 5 to get -50.

$$-\frac{1223}{12960}-\frac{6877}{2916}x+\frac{-50}{3}x-\frac{10}{3}\left(-0.4\right)=0$$

Fraction \frac{-50}{3} can be rewritten as -\frac{50}{3} by extracting the negative sign.

$$-\frac{1223}{12960}-\frac{6877}{2916}x-\frac{50}{3}x-\frac{10}{3}\left(-0.4\right)=0$$

Convert decimal number -0.4 to fraction -\frac{4}{10}. Reduce the fraction -\frac{4}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{1223}{12960}-\frac{6877}{2916}x-\frac{50}{3}x-\frac{10}{3}\left(-\frac{2}{5}\right)=0$$

Multiply -\frac{10}{3} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1223}{12960}-\frac{6877}{2916}x-\frac{50}{3}x+\frac{-10\left(-2\right)}{3\times 5}=0$$

Do the multiplications in the fraction \frac{-10\left(-2\right)}{3\times 5}.

$$-\frac{1223}{12960}-\frac{6877}{2916}x-\frac{50}{3}x+\frac{20}{15}=0$$

Reduce the fraction \frac{20}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{1223}{12960}-\frac{6877}{2916}x-\frac{50}{3}x+\frac{4}{3}=0$$

Combine -\frac{6877}{2916}x and -\frac{50}{3}x to get -\frac{55477}{2916}x.

$$-\frac{1223}{12960}-\frac{55477}{2916}x+\frac{4}{3}=0$$

Least common multiple of 12960 and 3 is 12960. Convert -\frac{1223}{12960} and \frac{4}{3} to fractions with denominator 12960.

$$-\frac{1223}{12960}-\frac{55477}{2916}x+\frac{17280}{12960}=0$$

Since -\frac{1223}{12960} and \frac{17280}{12960} have the same denominator, add them by adding their numerators.

$$\frac{-1223+17280}{12960}-\frac{55477}{2916}x=0$$

Add -1223 and 17280 to get 16057.

$$\frac{16057}{12960}-\frac{55477}{2916}x=0$$

Subtract \frac{16057}{12960} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{55477}{2916}x=-\frac{16057}{12960}$$

Multiply both sides by -\frac{2916}{55477}, the reciprocal of -\frac{55477}{2916}.

$$x=-\frac{16057}{12960}\left(-\frac{2916}{55477}\right)$$

Multiply -\frac{16057}{12960} times -\frac{2916}{55477} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-16057\left(-2916\right)}{12960\times 55477}$$

Do the multiplications in the fraction \frac{-16057\left(-2916\right)}{12960\times 55477}.

$$x=\frac{46822212}{718981920}$$

Reduce the fraction \frac{46822212}{718981920} to lowest terms by extracting and canceling out 324.

$$x=\frac{144513}{2219080}$$