Solve y=3/2(3/2)+2(3/2)^2-(3/2)^3

$$y = \frac { 3 } { 2 } ( \frac { 3 } { 2 } ) + 2 ( \frac { 3 } { 2 } ) ^ { 2 } - ( \frac { 3 } { 2 } ) ^ { 3 }$$

Solve for y

$$y = \frac{27}{8} = 3\frac{3}{8} = 3.375$$

Steps for Solving Linear Equation

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

$$y=\frac{3\times 3}{2\times 2}+2\times \left(\frac{3}{2}\right)^{2}-\left(\frac{3}{2}\right)^{3}$$

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

$$y=\frac{9}{4}+2\times \left(\frac{3}{2}\right)^{2}-\left(\frac{3}{2}\right)^{3}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$y=\frac{9}{4}+2\times \frac{9}{4}-\left(\frac{3}{2}\right)^{3}$$

Express 2\times \frac{9}{4} as a single fraction.

$$y=\frac{9}{4}+\frac{2\times 9}{4}-\left(\frac{3}{2}\right)^{3}$$

Multiply 2 and 9 to get 18.

$$y=\frac{9}{4}+\frac{18}{4}-\left(\frac{3}{2}\right)^{3}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$y=\frac{9}{4}+\frac{9}{2}-\left(\frac{3}{2}\right)^{3}$$

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{9}{2} to fractions with denominator 4.

$$y=\frac{9}{4}+\frac{18}{4}-\left(\frac{3}{2}\right)^{3}$$

Since \frac{9}{4} and \frac{18}{4} have the same denominator, add them by adding their numerators.

$$y=\frac{9+18}{4}-\left(\frac{3}{2}\right)^{3}$$

Add 9 and 18 to get 27.

$$y=\frac{27}{4}-\left(\frac{3}{2}\right)^{3}$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$y=\frac{27}{4}-\frac{27}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{27}{4} and \frac{27}{8} to fractions with denominator 8.

$$y=\frac{54}{8}-\frac{27}{8}$$

Since \frac{54}{8} and \frac{27}{8} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{54-27}{8}$$

Subtract 27 from 54 to get 27.

$$y=\frac{27}{8}$$

Assign y

$$y≔\frac{27}{8}$$