Solve 2{left(a/2right)}^3-a{left(a/2right)}^2+4a/2+10=0

$$2 { \left( \frac{ a }{ 2 } \right) }^{ 3 } -a { \left( \frac{ a }{ 2 } \right) }^{ 2 } +4 \frac{ a }{ 2 } +10 = 0$$

Solve for a

$$a=-5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\left(2\times \left(\frac{a}{2}\right)^{3}-a\times \left(\frac{a}{2}\right)^{2}\right)+4a+20=0$$

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

$$2\left(2\times \frac{a^{3}}{2^{3}}-a\times \left(\frac{a}{2}\right)^{2}\right)+4a+20=0$$

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

$$2\left(\frac{2a^{3}}{2^{3}}-a\times \left(\frac{a}{2}\right)^{2}\right)+4a+20=0$$

Cancel out 2 in both numerator and denominator.

$$2\left(\frac{a^{3}}{2^{2}}-a\times \left(\frac{a}{2}\right)^{2}\right)+4a+20=0$$

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

$$2\left(\frac{a^{3}}{2^{2}}-a\times \frac{a^{2}}{2^{2}}\right)+4a+20=0$$

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

$$2\left(\frac{a^{3}}{2^{2}}-\frac{aa^{2}}{2^{2}}\right)+4a+20=0$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$2\left(\frac{a^{3}}{2^{2}}-\frac{a^{3}}{2^{2}}\right)+4a+20=0$$

Calculate 2 to the power of 2 and get 4.

$$2\left(\frac{a^{3}}{2^{2}}-\frac{a^{3}}{4}\right)+4a+20=0$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.

$$2\left(\frac{a^{3}}{4}-\frac{a^{3}}{4}\right)+4a+20=0$$

Since \frac{a^{3}}{4} and \frac{a^{3}}{4} have the same denominator, subtract them by subtracting their numerators.

$$2\times \frac{a^{3}-a^{3}}{4}+4a+20=0$$

Combine like terms in a^{3}-a^{3}.

$$2\times \frac{0}{4}+4a+20=0$$

Cancel out 4, the greatest common factor in 2 and 4.

$$\frac{0}{2}+4a+20=0$$

Zero divided by any non-zero number gives zero.

$$0+4a+20=0$$

Add 0 and 20 to get 20.

$$20+4a=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$4a=-20$$

Divide both sides by 4.

$$a=\frac{-20}{4}$$

Divide -20 by 4 to get -5.

$$a=-5$$