Solve 16{left(3/2right)}^2-25+(2-3*3/2)(4*3/2+5)

$$16 { \left( \frac{ 3 }{ 2 } \right) }^{ 2 } -25+(2- 3 \times \frac { 3 } { 2 } )( 4 \times \frac { 3 } { 2 } +5)$$

Evaluate

$$-\frac{33}{2}=-16.5$$

Solution Steps

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

$$16\times \frac{9}{4}-25+\left(2-3\times \frac{3}{2}\right)\left(4\times \frac{3}{2}+5\right)$$

Express 16\times \frac{9}{4} as a single fraction.

$$\frac{16\times 9}{4}-25+\left(2-3\times \frac{3}{2}\right)\left(4\times \frac{3}{2}+5\right)$$

Multiply 16 and 9 to get 144.

$$\frac{144}{4}-25+\left(2-3\times \frac{3}{2}\right)\left(4\times \frac{3}{2}+5\right)$$

Divide 144 by 4 to get 36.

$$36-25+\left(2-3\times \frac{3}{2}\right)\left(4\times \frac{3}{2}+5\right)$$

Subtract 25 from 36 to get 11.

$$11+\left(2-3\times \frac{3}{2}\right)\left(4\times \frac{3}{2}+5\right)$$

Express 3\times \frac{3}{2} as a single fraction.

$$11+\left(2-\frac{3\times 3}{2}\right)\left(4\times \frac{3}{2}+5\right)$$

Multiply 3 and 3 to get 9.

$$11+\left(2-\frac{9}{2}\right)\left(4\times \frac{3}{2}+5\right)$$

Convert 2 to fraction \frac{4}{2}.

$$11+\left(\frac{4}{2}-\frac{9}{2}\right)\left(4\times \frac{3}{2}+5\right)$$

Since \frac{4}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$11+\frac{4-9}{2}\left(4\times \frac{3}{2}+5\right)$$

Subtract 9 from 4 to get -5.

$$11-\frac{5}{2}\left(4\times \frac{3}{2}+5\right)$$

Express 4\times \frac{3}{2} as a single fraction.

$$11-\frac{5}{2}\left(\frac{4\times 3}{2}+5\right)$$

Multiply 4 and 3 to get 12.

$$11-\frac{5}{2}\left(\frac{12}{2}+5\right)$$

Divide 12 by 2 to get 6.

$$11-\frac{5}{2}\left(6+5\right)$$

Add 6 and 5 to get 11.

$$11-\frac{5}{2}\times 11$$

Express -\frac{5}{2}\times 11 as a single fraction.

$$11+\frac{-5\times 11}{2}$$

Multiply -5 and 11 to get -55.

$$11+\frac{-55}{2}$$

Fraction \frac{-55}{2} can be rewritten as -\frac{55}{2} by extracting the negative sign.

$$11-\frac{55}{2}$$

Convert 11 to fraction \frac{22}{2}.

$$\frac{22}{2}-\frac{55}{2}$$

Since \frac{22}{2} and \frac{55}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-55}{2}$$

Subtract 55 from 22 to get -33.

$$-\frac{33}{2}$$

Factor

$$-\frac{33}{2} = -16\frac{1}{2} = -16.5$$