Solve (3.36)-15.876/4(3.36)+4447/3(3.36)^3-33391/2(3.36)^2+7.464(3.36)=

$$( 3.36 ) - \frac { 15.876 } { 4 } ( 3.36 ) + \frac { 4447 } { 3 } ( 3.36 ) ^ { 3 } - \frac { 33391 } { 2 } ( 3.36 ) ^ { 2 } + 7.464 ( 3.36 ) =$$

Evaluate

$$-132240.980256$$

Solution Steps

Expand \frac{15.876}{4} by multiplying both numerator and the denominator by 1000.

$$3.36-\frac{15876}{4000}\times 3.36+\frac{4447}{3}\times 3.36^{3}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Reduce the fraction \frac{15876}{4000} to lowest terms by extracting and canceling out 4.

$$3.36-\frac{3969}{1000}\times 3.36+\frac{4447}{3}\times 3.36^{3}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Convert decimal number 3.36 to fraction \frac{336}{100}. Reduce the fraction \frac{336}{100} to lowest terms by extracting and canceling out 4.

$$3.36-\frac{3969}{1000}\times \frac{84}{25}+\frac{4447}{3}\times 3.36^{3}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Multiply \frac{3969}{1000} times \frac{84}{25} by multiplying numerator times numerator and denominator times denominator.

$$3.36-\frac{3969\times 84}{1000\times 25}+\frac{4447}{3}\times 3.36^{3}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Do the multiplications in the fraction \frac{3969\times 84}{1000\times 25}.

$$3.36-\frac{333396}{25000}+\frac{4447}{3}\times 3.36^{3}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Reduce the fraction \frac{333396}{25000} to lowest terms by extracting and canceling out 4.

$$3.36-\frac{83349}{6250}+\frac{4447}{3}\times 3.36^{3}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Convert decimal number 3.36 to fraction \frac{336}{100}. Reduce the fraction \frac{336}{100} to lowest terms by extracting and canceling out 4.

$$\frac{84}{25}-\frac{83349}{6250}+\frac{4447}{3}\times 3.36^{3}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Least common multiple of 25 and 6250 is 6250. Convert \frac{84}{25} and \frac{83349}{6250} to fractions with denominator 6250.

$$\frac{21000}{6250}-\frac{83349}{6250}+\frac{4447}{3}\times 3.36^{3}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Since \frac{21000}{6250} and \frac{83349}{6250} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21000-83349}{6250}+\frac{4447}{3}\times 3.36^{3}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Subtract 83349 from 21000 to get -62349.

$$-\frac{62349}{6250}+\frac{4447}{3}\times 3.36^{3}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Calculate 3.36 to the power of 3 and get 37.933056.

$$-\frac{62349}{6250}+\frac{4447}{3}\times 37.933056-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Convert decimal number 37.933056 to fraction \frac{37933056}{1000000}. Reduce the fraction \frac{37933056}{1000000} to lowest terms by extracting and canceling out 64.

$$-\frac{62349}{6250}+\frac{4447}{3}\times \frac{592704}{15625}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Multiply \frac{4447}{3} times \frac{592704}{15625} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{62349}{6250}+\frac{4447\times 592704}{3\times 15625}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Do the multiplications in the fraction \frac{4447\times 592704}{3\times 15625}.

$$-\frac{62349}{6250}+\frac{2635754688}{46875}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Reduce the fraction \frac{2635754688}{46875} to lowest terms by extracting and canceling out 3.

$$-\frac{62349}{6250}+\frac{878584896}{15625}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Least common multiple of 6250 and 15625 is 31250. Convert -\frac{62349}{6250} and \frac{878584896}{15625} to fractions with denominator 31250.

$$-\frac{311745}{31250}+\frac{1757169792}{31250}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Since -\frac{311745}{31250} and \frac{1757169792}{31250} have the same denominator, add them by adding their numerators.

$$\frac{-311745+1757169792}{31250}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Add -311745 and 1757169792 to get 1756858047.

$$\frac{1756858047}{31250}-\frac{33391}{2}\times 3.36^{2}+7.464\times 3.36$$

Calculate 3.36 to the power of 2 and get 11.2896.

$$\frac{1756858047}{31250}-\frac{33391}{2}\times 11.2896+7.464\times 3.36$$

Convert decimal number 11.2896 to fraction \frac{112896}{10000}. Reduce the fraction \frac{112896}{10000} to lowest terms by extracting and canceling out 16.

$$\frac{1756858047}{31250}-\frac{33391}{2}\times \frac{7056}{625}+7.464\times 3.36$$

Multiply \frac{33391}{2} times \frac{7056}{625} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1756858047}{31250}-\frac{33391\times 7056}{2\times 625}+7.464\times 3.36$$

Do the multiplications in the fraction \frac{33391\times 7056}{2\times 625}.

$$\frac{1756858047}{31250}-\frac{235606896}{1250}+7.464\times 3.36$$

Reduce the fraction \frac{235606896}{1250} to lowest terms by extracting and canceling out 2.

$$\frac{1756858047}{31250}-\frac{117803448}{625}+7.464\times 3.36$$

Least common multiple of 31250 and 625 is 31250. Convert \frac{1756858047}{31250} and \frac{117803448}{625} to fractions with denominator 31250.

$$\frac{1756858047}{31250}-\frac{5890172400}{31250}+7.464\times 3.36$$

Since \frac{1756858047}{31250} and \frac{5890172400}{31250} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1756858047-5890172400}{31250}+7.464\times 3.36$$

Subtract 5890172400 from 1756858047 to get -4133314353.

$$-\frac{4133314353}{31250}+7.464\times 3.36$$

Multiply 7.464 and 3.36 to get 25.07904.

$$-\frac{4133314353}{31250}+25.07904$$

Convert decimal number 25.07904 to fraction \frac{2507904}{100000}. Reduce the fraction \frac{2507904}{100000} to lowest terms by extracting and canceling out 32.

$$-\frac{4133314353}{31250}+\frac{78372}{3125}$$

Least common multiple of 31250 and 3125 is 31250. Convert -\frac{4133314353}{31250} and \frac{78372}{3125} to fractions with denominator 31250.

$$-\frac{4133314353}{31250}+\frac{783720}{31250}$$

Since -\frac{4133314353}{31250} and \frac{783720}{31250} have the same denominator, add them by adding their numerators.

$$\frac{-4133314353+783720}{31250}$$

Add -4133314353 and 783720 to get -4132530633.

$$-\frac{4132530633}{31250}$$

Factor

$$-132240.980256$$